Is this considered normal and professional?

Not normal. Very unprofessional. I also worked with 3 agencies. That was the only way I could ensure coverage.

There are a lot of flaky people that work in this industry.

Just push forward.

That was wrong on all counts

Sadly, it probably is “normal” but certainly not professional. As you said, it is a “temp agency,” so changing caregivers and agencies would be a very regular occurrence. It was this particular aide who was unprofessional and the temp agency can still provide aides through the transition.

What does the original contract with that agency say about it?

I understand that most aids want a minimum of 30 hours per week per client, and this is much easier in terms of scheduling aids. But just quitting like that is definitely unprofessional and shocking.

I would contact them and say if they don't figure out a better solution you will be informing people on Nextdoor.com about this terrible experience. If the agency admins have a brain they will scramble to make it right.

Then again, maybe it's better that they fired themselves. They showed who they really were, so best to believe them.

Depending on the country, that’s criminal, to be reported to the police. Abandoning a helpless, elderly person.

The temp agency should find a new person. But they won't unless they think they will get more work from you. If there not getting a possibility of more work then they won't care. It's all about the money .

I'm not sure about "normal" but in my experience lots of changes occurring in scheduling has occurred with my dad, using 3 different agencies. In the beginning they nod their heads about the importance of consistency with caregivers, but in time, with all three I found people starting changing up. NOW, my dad is VERY DIFFICULT to work with, so that is a factor I'm sure also.
On the other hand, I think some caregivers do want a minimum number of days of regular work, even via agency. So maybe that is a factor for you?