First, it is more likely that the bank would remove your dad from the account rather than freezing it entirely, as it is a joint one held with your mum. In essence, this just means that your dad would no longer be able to access it. It is correct that banks can - and do - freeze the accounts when they believe that the holder no longer has the capacity to manage their affairs.
This is to protect the holder and the bank, which could ultimately end up liable should the holder, for example, run up large overdrafts and become bankrupt or pass away with their estate being unable to settle the debt.
Your mum should arrange to meet with the bank, at managerial level. It is much better to reach mutual agreement than for the bank to remain in the dark until it ends up taking pre-emptive action. It is almost certain that a suitable arrangement can be made.
I am extremely surprised, and shocked, to hear that anyone would be advised against making a power of attorney whilst they have the capacity to do so. It is one of the best things anyone can do. They are usually set up so that they can only come into force (be registered) when the person making them (called the donor) loses mental capacity. The donor can nominate whoever they wish to be the attorney (the person who gains authority to manage the donor's affairs) and obviously this is someone they trust implicitly. In this case your mum would be the obvious candidate. The donor may confer powers to make decisions on either financial or health matters, or both, although the latter are more limited in scope whereas the former cover almost anything (unless the donor specifically excludes some powers)
If there is no power of attorney, and the donor has lost capacity, they cannot then create one. Instead, the potential attorney has to make application for deputyship through the Office of the Public Guardian. A deputy has authority to manage someone's affairs although this is usually confined to financial matters. This process is more complex, time consuming and costly as the OPG must rigorously check that the donor has lost capacity, that tghe deputy is a suitable person, etc.
In the meantime, it is possible for someone to apply to become an appointee. This means they can apply to the Department of Work and Pensions (DWP) to manage someone's state benefits - but only those. For example, state pension. As an appointee your mum could receive your dad's state pension and use it to pay bills, etc. Becoming an appointee is relatively simple: the DWP will investigate to satisfy themselves that the person actually has lost capacity and, of course, that the appointee is a suitable person. It usually involves nothing more than an informal interview with said parties and, as far as I am aware, there is no fee.
If your dad goes into care this complicates matters. Much depends on whether he will be self-funding or not - this depends on the outcome of the financial assessment.
As part of this, his assets would be calculated as including 50% of anything he has in joint names with anyone else. The home would, however, be excluded as his spouse (mum) lives it it and would be so protected so long as she lives there. If he is self-funding then his income would be included, although 50% of his occupational (ie, non-state) pension must be reserved for his spouse.
If your dad goes into permanent care, then your mum would be regarded as effectively single in regard to state benefits. This would mean she might, for example, become elligible for Pension Credit, depending on her income. It is often the case, for the older generation, that women are dependent on their husband's income having little of their own since they have little to no occupational pension and have not paid National Insurance. However, as I said, if their husband goes into care they are assessed as single for benefits purposes and thus may become elligible for means-tested payments that they could not receive as a married person.
Lastly, it is reasonable for your mum to use the money in the joint account for upkeep of the home, for example, having repairs done. The usual test that is applied is that it is "normal expenditure" (as opposed to, say, suddenly going on luxury holidays) and that would have taken place if your dad had been well and living at home.
It is very unlikely to be regarded as a Deprivation of Assets (this means, spending or giving away money in order to evade being liable for care fees)
However, it might be wise to seek advice from the local authority or social services - in writing if possible.
The bank itself is unlikely to freeze the account for this reason, since as far as they are concerned, money in a joint account is entirely owned and at the disposal of both joint holders regardless of who actually paid it in. Likewise, each account holder is held responsible for any debts that are run up using the account regardless of which holder ran them up.
This is why, of course, banks always tell customers to use caution when setting up joint accounts.
