Like there are hundreds of tutorials and walkthroughs while setting up your own bitcoin wallet even if it's an SPV client like Electrum. My point is, anything typed/saved on the web is quite prone to numerous attacks especially if one is a noob. Better would be to install a desktop client and it's not that hard!
Imagine if blockchain.com's servers go down tomorrow. A hypothetical situation but only the ones with their private keys would be able to recover their monies back.
Ah, I thought you were referring to Core only. I personally wouldn't run Core myself. My internet is too sketchy to run any type of node and the download would take several days.
Yup, there are plenty of other options beyond blockchain's offering. Unless you have an old blockchain wallet you'll have your seed that you can take elsewhere if they crap out.
The wallets that truly blow my mind are the handful that still don't give you private keys such as Freewallet, let alone Coinbase and Xapo of course. Why anyone would go anywhere near them is an absolute mystery.