A web wallet is one such wallet. You do not need to use any additional applications to save it. It is much safer. In my opinion, web wallet is much better than mobile wallet. Using it does not require a separate space. Hopefully the wallet will expand further in the future.
I agree, most of the exchange and wallets are made as a website and the applications are more like an extension of the wallets, so it's definitely safe and better to use a web wallet on your computer.
There are also some that offer android applications that you could also use, not all wallets have a mobile application so it might not be optimized when opening on the mobile devices. Also you just need to be aware of so many phishing and scam applications that trying to copy legitimate wallets. You could just check the web wallet website if it has a mobile application.
But both platforms have their advantages and disadvantages because mobile devices are portable.