I think it's a good idea to use more than one bitcoin wallets.I use 2 wallet for security purposes. many people get hacked.
If one wallet website get hacked, you have another wallet as an backup.
Of course for security purposes one should not store all his bitcoin in a single wallet most especially if the wallet is an online type because it can be hacked at at any time. it is advisabe to split it so that whatever that comes up you are rest assured to be safer always. Compared to web wallets, desktop/hardware/paper wallets very much safer, having all of them will give extra protection significantly.If one wallet website get hacked, you have another wallet as an backup.
A lot of people actually stores all their coins in one wallet, if that wallet is a hardware or paper wallet then that can be quite safe but as you mentioned if that wallet is an online wallet then it is really not a good decision to put all your eggs in one basket, if the basket is stolen all your eggs are gone
better to keep them in different places to save most of them.