You do have a choice OP and by accepting LPA you are making the choice to be involved at least to some extent. If you don't want to be, then pull the plug on that and leave it to SS to sort things out. This won't necessarily be any easier on you, as you'd have to walk away from your dad, but it's still your choice.
Have you applied for Financial and / or Health & Welfare LPA?
If he has capacity, he decides where to live. SS can make an assessment but unless he has lost capacity he won't be forced to move irrespective of what they recommend. They will also do a financial assessment and decide if he is self-funding or not. He or you will have to provide the financial information to allow them to make this assessment - so (especially if you are going to be his attorney), you need to get into his paperwork and his bank accounts and find out what's what.
SS care assessment should take into account his living conditions, but there are many options between living at home and going to a home. e.g. can he sleep and toilet downstairs if a commode is provided (carers would empty it)? Is there a bedroom / room that could take a bed downstairs? Again, if he has capacity, he decides what happens - for better or worse. This is usually where adult children get sucked in - trying to make changes or provide support that enable the EP to live at home, in an increasingly unsustainable manner, until the wheels come off and a (usually medical) crisis happens. At which the EP ends up in hospital, and everything needs to be reassessed depending on the condition they are in when they leave.
Have a think with your dad about the following aspects of care that can be provided by carers up to 4 times a day:
Medication given
Help to wash / dress / toilet / undress / ready for bed, morning and evening
Food served / fed and cleared up
Drinks served / given
Ask yourself what does he need help with and can it be done, given the house layout? The SS assessment can also propose adaptations such as bars to hold, mobility aids etc.
The things that carers / SS generally won't do are:
Cleaning / housework
Laundry
Ordering medication
Making / getting him to medical appointments and keeping on top of these i.e. chasing referrals etc
Sorting out administration / general life - paying bills, buying clothes etc.
Ask yourself how these will be dealt with if they aren't already?
My MIL had Parkinson's plus other conditions. She stayed at home with help from family until she was unable to walk and no longer continent. She never had carers, but FIL unfortunately wasn't a great carer at home - she hid her medication, didn't eat much, didn't drink etc. so ended up delerious, in hospital and went straight to the nursing home from there.