What is the potential thought process that makes my 82-year-old mom no longer desire to be self-sufficient and/or independent?

Does aging automatically make us have disregard for other people? I don't think so! I'm in my 80's, have been independent my whole adulthood. I hate asking for help.

But I also hate the fact that I no can no longer drive. I have to do a lot of advance planning to accomplish basic shopping, haircuts, a needed trip to the post-office, getting clothes to the cleaners of even the GoodWill, visit to my attorney, my doctor, the bank etc.
I'm not as quick-thinking as I used to be and if I move at what seems a normal speed for me, the body doesn't always co-operate. Sometimes I fall. Falls didn't used to bother me, but that was because it was easy to get up and keep going. Now it's difficult to get up and I risk breaking a hip like other elderly people I know.

Actually, life is a lot more convenient these days with the internet and credit cards. But I didn't grow up with internet. It's an ever changing world online and I'm not very skilled at handling it. Oh, I used to have pretty good control of things...but nowadays not even my bladder cooperates (now, that's embarrassing). Nor do my arthritic hands that used to easily sew on a button or fasten a necklace behind my neck.

I used to have friends with whom I could commiserate. We would laugh about our difficulties, swap tips for getting things done. But most of them are gone now, dead before I was ready to say goodbye. And I miss them.
Sorry if this sounds like a sob story. I know young people have children, homes to care for and multiple tasks at work... many social obligations, too. Been there, done that.
I hate asking for help, busy as they are, but I just sometime see my life falling away in little pieces and there's not much I can do about it.
I try to express how grateful I am for any help someone can give. It's often a sacrifice for others, but I hope they never feel unappreciated!

You say "why do we........" but the fact is we are not all like your Mom. I am 80. Neither of my children live anywhere near the state I live in. I determined to make myself independent of my children and I in fact do all I can to minimize any worry they may have, and to reassure them.
This is what my parents did for me as well.
We are all individuals and we are as unique as our own fingerprints.
Good luck out to you.

If this is a "new" behavior for your mom, then I would assume it's related to a change in cognitive status and not "age related decline."

My mother was the most considerate person on the planet, and then she wasn't. In turned out that she'd had a stroke that had taken out most of her executive function and planning ability. So she just kept asking us/telling us to do things. But we had jobs!

She also mis-understood EVERYTHING her doctors said to her.

So maybe this isn't manipulation
Maybe she isn't reasoning/understanding stuff.

I'm not in my eighties but I've noticed how a multitude of little things that I used to do without thinking have become increasingly more challenging, and I'm no couch potato. I think that we often fail to take into account just how hard even simple tasks may have become for someone who is older and how exhausting just living can be, especially for those who are perhaps not terribly fit. Imagine coupling that with the feeling life has passed you by so why keep fighting, or perhaps a cultural creed that says elders are to be pampers and waited on.🤔

I think age brings an acknowledgment of loss of skills, some of which are too challenging to overcome, or are activities in which people have lost confidence in their ability to handle.

I think you'd need to consult a medical person, perhaps a psychologist or psychiatrist focusing on aging, to address a declining or loss of self sufficiency. 

There's also the blunt and perhaps frightening recognition that age has or is compromising us and we do need to seek help.  Or someone could just be tired and worn out from the challenge of aging.  

As to "hating to inconvenience people", I think that could be more than just inconvenience, but rather, arises from a survival concept.

I suspect one's existing personality, upbringing, and the examples we've seen over our lifetimes all play a role in how we react to temporary or ongoing infirmity and loss of abilities. Some people as they age are willing to reach out and pay for things they can't do for themselves, but still have a sense of control and autonomy so they don't feel "beholden" to others for voluntary services. Others may take help for granted and do seem to lose the ability to see that they are in fact putting out, "inconveniencing," those who are helping them. I had two long-lived grandmothers who were very independent, and my parents were likewise. Like Alva, I'm determined not to be reliant/dependent on our children and we've planned accordingly. We do have several kids who live nearby and who do nice things for us, e.g., bring over meals or goodies, but we want them to live their own lives and not be tied down by us.

The honest answer is that it really depends on your mom.
Is this new behavior? If so she could be depressed. She could have pain that she isn't telling you about. She could possibly have a UTI. She could have some new diagnosis that needs to be explored including dementia or even something else physical.
If it's not new, you may need to explore when the behavior really started. Without too much detail, we've dealt with this with my FIL for a long time due to a personality disorder. He has long believed that he was owed many things. He has been waited on hand and foot by a number of enablers but for most of his life he didn't have pain that went along with it so he still did for himself. As he aged, a number of comorbidities piled up and began to cause him pain and one thing he cannot tolerate in the slightest is pain of any kind (that is not meant to sound insensitive, he can't tolerate so much as a stubbed toe without a trip to the ER, he just doesn't do pain at all) So when doctors, nurses and physical therapists advised movement to alleviate pain and maintain mobility and independence he shut that down and did the opposite and insisted that he be waited on and unfortunately he was in a situation to be obliged. He was warned that this would eventually lead to him losing his mobility entirely and I believe he thought that when he was ready to get back up he just.....would? Now...well it's no longer a matter of won't.. it is a matter of can't.
So that's the long answer. I think for some people, if there are no underlying reasons why they have shut down, they honestly don't think there will be any repercussions to stopping until they can't get back up...they spend all of that time not doing anything thinking that when they decide to get back up and do they will just pop right back up where they left off and go right back to how they were. And part of it is a little bit of denial maybe. And part of it is that it isn't as easy, so it's just easier to NOT do it? But it is better if they can to keep doing anything they can as long as they can. Because once they stop, it's very difficult to get it back and takes twice as much effort.

Initiative. It goes away when there is cognitive decline.

She may not be ABLE to even figure out how to accomplish tasks on her own, or with others’ help.

As her child, she may still, though, be able to know that you are a helpful person who can get things done.

It’s EXTREMELY frustrating to those around the elder. I’m sorry.

As for your friend, it doesn't sound like he's a quick learner.........LOL!!!! Perhaps friends can get together and build him a deck?

As for mom, it sounds like she's ready for Assisted Living; she's lived a long life and probably deserves to be assisted each day and not expected to perform duties/chores. Perhaps you can take her to visit some Assisted Living sites to see if she likes them. Life is always changing and the aging process reminds us that the "clock of life is ticking."

My mother went in the other direction due to her dementia. She was always independent, but with the dementia, she would get angry if anyone tried to help her. If she could not do something, she would not let anyone else do it, and then not do it herself. She would not let caregivers clean the house, wash her clothes, throw out old food, etc. Eventually, we had to move her to a memory care facility, where she complains bitterly about her lack of independence. But she is safe and in better health now.