What are some of the ADLs necessary to keep a parent at home?

Because this is a common question, AgingCare has an article, including a printable assessment, to evaluate a parent's abilities when deciding if they are able to safely age in place. I hope this helps:
https://www.agingcare.com/articles/should-elderly-parent-continue-living-at-home-95665.htm

ADLs for a loved one to stay living at home are different from one caregiver to the next. There isn’t a set rule that a person must go into care when they can no longer perform ADLs although they must be deficient in ADLs before they can be approved for some facilities.

The list, however, is what I have used many times to assess where my loved ones were in their ability to live “independently”.

Almost everything that can be done in an ALF or even a NH can be done in a persons home depending on manpower, finances and the willingness of the caregiver to continue home care. Many things can be done much better at home.

Since you have two sisters who share the care you might continue longer than an “only” caretaker. Not that you must.

For me personally when a person can no longer transition themselves, that would be an emergency placement. Others would use a lift.

Personal toileting or bathing are not chores I ever intend to take on if I have a choice. Others on this forum take that in stride.

Always remember that you have to advocate for yourself. You don’t have to use ADLs as a reason to be or not be a caregiver. Your life matters just as much as your father’s.
And so does your sisters. While it’s great to have sisters that are all in, I can see where it could be stressful if they wanted to keep him home and you didn’t. Each persons life must matter regardless of ADLs.

Im sorry if I missed the point of your question.

Even if the senior seems physically pretty fit and mobile, short-term memory loss was the deal-breaker in our situation. Even though we lived only 6 miles from my MIL and were providing meals and groceries, we discovered she was not eating because she THOUGHT she had already eaten. Once we were together at a social event and she was faint, which was odd. Upon checking her fridge, sink and garbage, there was no evidence she was eating. Her fridge was full of rotting food, even though much or it only required to be heated in the microwave, which she has used her entire adult life. When I would call her to quiz her on what she ate and how much, she'd tell me specifics. But upon going into her home NONE of what she said was true. Also, she wasn't taking her thyroid medicine, or was taking too much of it. In prior years she was on opioids for a post-back surgery. SHe kept running out of her meds. We eventually put 2-and-2 together. She could chit chat very general conversation and you'd never know she had an issue. But if you asked her who was the president or what season are we in...she could look out the window and not be able to give an accurate answer. This is a long way of me saying not to take things at face value when you talk to your parents. If something seems off, more thorough checking must be done. Good luck!