Does Ledger Wallet is still usefull and safe if we can not manage our accounts anymore with it?
I keep saying that ledger wallets are dog shit, especially if you are using them for any shitcoins that all have different derivation paths and they could be incompatible.
They had problem with some coin apps in past, or update could make impossible to sign transaction, and there is no fix for that except waiting for devs to update.
Your coins should be safe if you store backup words in safe place, and I guess you could always try importing them in other wallets.
You could try to reset and uninstall than install everything as a last step, if you didn't do that already.
Is there better harware wallet at this time?
There are much better hardware wallets, that are open source, but I am not sure how many of them are supporting shitcoins like Dogecoin.
I am sure that Trezor One and Trezor Model T support coin you want, but I would suggest adding passphrase to make your account more secure.
Good thing about Trezor is that there is no separate app for each coin and that usually means less issues.