Why would they still have access to wallet B if they lose access to wallet A? If, for instance, you keep wallet B in a different location than wallet A, why don't you just keep a backup of wallet A on the same location?
Because you have to secure it a lot and you can not prepare well for
loss or
stealing of your private keys.
What's the problem with the current non-custodial Bitcoin?
1. You have to take care of your own seed / private key.
2. You have to store it in a way that nobody could even access the seed, if somebody finds your seed even for a second, he / she can spend it and there is nothing you can do to stop this.
3. If you leave your key somewhere and somebody accesses it, you will not even find this out. So, a thief could spend all your balance immediately or he can wait for days, weeks, months or even years to spend everything you accumulate over the time. If you give me your 12 words seed phrase there is no way you can now if I did something with the words until I wipe out your wallet. For example you have 0.01 BTC now, and a thief will wait until you have it least 1 BTC and spend everything only that time. You think that everything is OK, while in fact somebody is already watching every move you make and just waits for the right time to rob you.
4. Based on point 2 and 3, you really have to hide the seed in a place where nobody can access it (by putting a camera with motion sensors in the room where you store it), as soon as somebody enters the room and potentially see the seed, you have to act fast. From that moment it is a matter of who is faster on spending the funds, you or the thief.
5. If you decide to put the seed to 2 different places to protect from loss (for example one in office safe and one in home safe) just to make sure that if a fire, flood or any other event destroys one of the seed copies, you still have the other one for backup. This is practically double your efforts on point 4, as this time, you have to protect 2 places. More backups, mean more safety precautions!
6. Too many precautions (for example splitting the seed phrase in 2-3-4 locations) will limit the chances of being robbed but can also lead to loss of the seed. Remember, for example if you split your seed phase and store it this way A-B-C-D-E-F (location 1), D-E-F-G-H-I (location 2), G-H-I-J-K-L (location 3), J-K-L-A-B-C (location 4), this has a 1/4 fault tolerance, so if somehow you can't access one of the locations you are still safe, but if you can't access 2 locations from 4, you already have a problem as your seed is gone.
With the proposed solution what you will need:
1. a non custodial wallet where you will hold all your bitcoins (wallet A to be backed up)
2. a custodial wallet where you do the KYC but not hold anything there (this can also be another non custodial wallet) (wallet B where we send your coins if you need to activate backup)
3. an account with us that you will use in case you lose your access to your non custodial wallet (wallet A)
So, basically all your funds will stay forever on the non-custodial wallet but you will need wallet B only if somehow you lose the private key / seed phrase of wallet A. In this case, all you have to do is to login to the backup service and use the previously signed raw transaction (you signed it when you could still access your keys) to send all your funds to your wallet B. Since, wallet B is a custodial service (which is an advantage in this case), for example Coinbase, Bitstamp, etc., you simply login back to this service and voila, you have your bitcoin on the wallet B. If, for some reason, you forget the login and password for your wallet B, with proper KYC proof, they will let you in, and your funds will be safe. Of course, after this is done, you simply withdraw your funds from wallet B to a new wallet you are creating just to not keep your coins on an exchange.