I use blockchain wallet and so far had no issues. But there is no 100% guarantee that it will not be compromised. So, it's better not to keep all your coins just in one wallet and also to have something in cold storage, especialy the larger amounts.
The online wallet no 100% guarantee
yes, you are right. don't stored yor all coin in the online wallet it is not safe. Good choose to save it in hardware wallet or paper wallet.
Once you get beyond the beginner stage, I would say this may be a typical advanced user setup. Not everyone does this, but think of power users and people that are really invested in bitcoin.
1) Have an online web wallet that syncs to your mobile app for on the go spending (read that as not all your funds in this wallet)
2) Have a desktop client program on your local machine for a good chunk of your funds that go to your spending wallet to refill.
3) Have a hardware wallet for all the rest of your bitcoin for savings and safe keeping and best security.
Of course all need to be regularly backed up.