This is one of the advantages to having a multi-sig wallet where you need multiple keys to sign a transaction instead of just one. Having a single key represents a single point of failure. Of course you still need to manage your keys in a multi-sig setup, but you don't risk ruin if you happen to lose one of the keys (if for example you had a 2 of 3 setup which means you have 3 keys but need only 2 to sign a transaction).
Just for the purpose of a safer backup, you don't necessarily need a multi sig wallet.
This just makes any transactions bigger in size and therefore more costly.
I mean, that's definitely an option and better than a single point of failure. But i'd prefer a secret sharing scheme over multi sig as a backup spread between multiple locations if N out of M pieces should be required.
The upside is that you can basically store any sensitive information that way. Private keys, mnemonic codes, passwords etc..
And always the property holds that if someone has N-1 shares, no information about the secret is leaked.