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Not really, among "normal" banks. This does seem to be the case with the new "challenger" banks like Monzo and Starling, which are all "mobile first" and are basically impossible to use if you don't have an Android/iPhone. But every regular bank in the UK has a website with online banking, often with more functionality than the apps, but maybe this is different in other countries - online banking in the UK has been commonplace since before mobile apps were really a thing.

Funnily enough, my last bank and two current ones, the app is increasingly a front for a mobile web version. With each new update I see more functionality moving to web.

What are some American banks that don't have a website but have an app? I'm curious.

BofA, the bank that most Americans use, doesn't support mobile check deposit outside of the native app.

I have an account with Bank of America and was not aware of this so thanks. That said, you can do pretty much everything else via the website. The opposite is also probably true, that there are some features on the website not available on the app (for example can you open a new CD in the app?).