Yes, even if the recipient thinks they will eventually have the legal right of access, until they do it's not legal to try and move funds.
For a couple, this is one reason to think carefully about which assets are in joint names and which are separate. Ideally, they should have enough money in joint, liquid accounts to cover however long it may take to be granted probate.
I can only speak for the UK, but here, there are two types of power of attorney: the health one designates someone to make decisions about medical treatment if the subject is unable to; the finance one allows the attorney to manage the assets of the subject when needed.
The key point is that the whole process should be far easier if these things are setup in advance, while the person is still able to make their wishes clear, i.e. while they can still say who they trust to make decisions for them.
Fundamentally, the OP isn't faced with a tech problem. People need to start with greater awareness of power of attorney, wills, and probate.
In a probate situation, your loved ones don't have to know all your passwords and so on. They do need to know where your assets are so they can contact the right organisations to claim them. And you can make that process easier for them by avoiding having small accounts all over the place.