I can't online every day because I work at a mine site where there is no internet connection (sometimes more a month I am offline), this makes me have to choose the best wallet and can solve the problem when it happens, and from my experience the best web wallet is coinbase and xapo.
Also if you use hardly or a long term investor then better to switch to the offline mode as it will help you to keep the scammers away from the wallet who look to scam it. Just in case if it is not too much coins then it is fine to keep in online wallet.
You are right, I personally don't trust in any web wallet to store a huge amount probably small amount will be fine but for long holding coins, I must prefer hardware wallet or those offline wallets like Trezor or Ledger Nano these wallets now most likely used others and most trusted to them to store a huge amount of bitcoin, no doubt on this. Web wallet is worth it and 99% of your fund is secure if you have different keys to hold like 2FA authentication I fell safeguard on that.
