I can't remember how many old wallet files I've deleted from Phone and PC so far, but I can absolutely confirm that they won't be of any value anymore as no assets are stored on any of them.
But why? You can't be 100% certain you won't accidentally reuse an old address in the future, or someone who sent you coins to one of your old addresses won't send coins to that address again in the future, assuming you still have access to it. If it's a wallet on your phone or PC, as you say, then you have nothing to lose by keeping a copy just in case. The file will be few megabytes at most. In the words of Satoshi:
Sigh... why delete a wallet instead of moving it aside and keeping the old copy just in case? You should never delete a wallet.
The other way around this issue is to use full disk encryption, which I use on all my devices. If you use a strong enough decryption key, then it doesn't matter if you leave some data behind after shredding, as it will be meaningless to anyone who is able to recover it.