That's not true. Many custodial wallets have different methods for their users to log into their accounts and access their funds. Losing your device or having a problem with it wouldn't mean you have lost your coins unless the user also loses access to the method he used to create the account such as an email address or something. If someone has created a wallet account using an email address, they might be able to reset their password using that email address on a new device and get access to their funds.
It seems you are misinterpreting my post. I'm not talking about the method to access whatever platforms Op uses to store his funds but rather, I'm concerned about the funds specifically. Op stated that the wallet did not display seed phrase which is the genesis of the problem. No one would have bothered about faulty device or the old wallet is accessible or not if he has the seed phrases. I will still repeat myself, if you don't have the keys, the coins is not entirely yours.
While we are waiting for OP to tell us the name of the crypto wallet he/she is referring to, that didn't allow him/her to view it's seed phrase, I was able to make my own personal research, and I got to discover two wallets, namely "Nami Wallet" which is claim to be non-custodial browser-based wallet extension for Cardano blockchain which is used for sending and receiving of all Cardano tokens and assets, and doesn't allow display of wallet seed phrase, whereas, another wallet that doesn't have seed phrase is "Zengo wallet" which happens to a self custodial crypto wallet which supports Bitcoin and all other coins, such as Ethereum, BNB, & others.
So is any of the two wallets I mentioned the one you were referring to?
What made them non custodial wallet then? They claim to have no access to seed phrase and likewise the user have no access to seed phrase, who then possess the seed phrases? And how do they expect one to access their funds outside that wallet? Seed phrase can not just be in the air, either the platform or the user must possess the seed phrases.