Sorry that you feel that way about S/Workers. They do care, but are struggling to cope with under-funding, not enough of them, and being demoralised at every turn by the opinions of people who only see one side of the coin.
I have been a s/worker, and have been a service user both for my MIL, and for myself.
In order to get the care that you needed, you should have told the AE dept, that you could not take your mother home, as there was no care available for her. Sadly, this would have meant that she would have been in Hosp. over the Christmas period, but she would have been in the system, and would have been sorted eventually [along with the hundreds of other elderly people vying for the small amount of money available] Once assessed, she would [depending on her ability both to function, and to pay] been found the care which was deemed 'correct' If this was deemed enough to have daily/twice/3 times a day visits, that would have been put in place,[plus a statuary financial contribution from her], if she needed more care, then her finances again would be assessed, and sorted accordingly. This means that property, money, bank accounts will be sold/emptied, until either she gets down to the basic money allowed, or she dies. This is how it is. Sadly you do seem to have a very idealist & naïve view of life, from what you had written it was almost as if having rung SS on Christmas Eve/Day/Boxing day, you expected someone to be just waiting to take your call, instantly sort out your problem, and say, 'all done now, go off and enjoy your Christmas?' Get real. You are expecting to have a life after work, s/workers also have a life, and possibly families, which they organise, in order to go and try to help someone else sort out their lives/families/parents/children. They are not sitting just waiting for a phone call, the are too busy sorting out the people already in the system. however, see your GP, rrange an assessment, & Take a day off, in the short term you could buy a keybox, you could look at care agencies, whilst you are waiting, failing that, ext time your parent has a fall, call the ambulance, and then leave it to AE to sort her out, and say you cannot care for her yourself, as you are in full time work/cannot manage/have time off/etc, then as has been mentioned before she will be in the system, and will work her way through with the help of s/services/social workers. This is not being cruel, it is being realistic.
I usually feel that most people balk at the bit about finances' seeming to feel that there should be an 'inheritance' of sorts left at the end of it all?