You gave very good suggestion it is really important to keep our seed phrase safe because splitting it up is big risk if lose even one piece we lose access to all our funds.
Smart way to protect it is by adding passphrase. We can store our seed phrase and passphrase in different spots making it much harder for someone to get to our money even if they find one part.
Wallets can be created with or without wallet passphrase but the bottom line is you must make your wallet backups good enough and in a right way.
If you don't back up your wallet passports but only use your brain and memory for remembering it, it is very dangerous backup method. No guarantee that your brain and memory will not have problems that cause terrible memory loss of your wallet passphrase. If it happens, you will lose your wallet and bitcoin except if later you manage to recall the wallet passphrase for recovery.
So, splitting your wallet seed phrase or not, using wallet passphrase or not, you must back it up properly.