Is AL or LTC home a good option for a 96-year-old who is falling a lot?

You live in Canada if I am not mistaken?
If he falls call 911, social worker will come in hospital to talk to you and grandfather. They will advise and assess his mobility, get PT and OT to assess his condo. He might need bars in shower, toilet, removing rugs etc.
It is possible he cannot live independently.
Get home care involved which is free for everybody in Canada.
They have social worker or case workers and if I am not mistaken LTC arranged thru them cost less $2700 per month. They are tremendously helpful.
They arrange services such as day programs, showers if needed, help with exercises, respite, transportation for appointments and many others.

Don't move in with him. You have gone above and beyond, he needs to be placed , and you can give him care there, visit him and do errands for him.

But you deserve your own life.

No facility can "make" him stay in a wheelchair as this is considered "restraint" which is abuse. He will just get up and fall, get up and fall, until one fall will be the one that breaks his hip, or worse. This is a common scenario and not much to be done about it.

I agree wholeheartedly with the advice to not move in with him or move him in with you. You will become his 24/7 caregiver and a lot in your life will come to a screeching halt. The next time he falls, do not pick him up. Call 911 and have him transported to the hospital. Then make sure the discharge team knows he's an unsafe discharge. Find a facility for him and have him transitioned directly into it (he might go to "rehab" first but make sure he has a facility to go to after that. It's hard... I'm sorry for this distressing situation.

Yes, it is. You may want to consider a Board and Care if you can find one. Much more homelike atmosphere, often run by families and often only about 6 people with own rooms and good home cooking. The thing to know and understand is that elders will and do fall and at 96 they often do it with great frequency. A fall CAN and often does spell the beginning of the end (it did for my own mother) but there is little to be done about that. The falls are not often due to weakness or dizziness but due to brain changes that cannot be fixed.

Someone from AL that you choose will come and assess him and tell you if they are willing to take him in AL . Then you will know if he needs a higher level of care ( SNF ) .

What does his doctor say?
In the US I called the County Area of Aging for a social worker to assess my mother , I could not get Mom to leave her home to go to AL. They were willing to remove her from the home and bring her to an AL that I had chosen .

Can you call a social worker there to help ?

The next time grandpa falls don’t get him up . Call 911 or whatever it is in Canada to get an ambulance to take grandpa to the hospital , then tell them you can’t care for him anymore and he needs to go to a facility. Do not pick him up from the hospital . Do not take him home , even if they tell you it’s temporary . You tell the hospital that it’s an “ unsafe discharge “ for him to go home. Use those words , because they will try to make you take him home . Tell them he lives alone , falls all the time and you can’t take care of him . Do not tell them you live with him or stay with him . Tell them you have to go back to the US to go back to work .