I only ever use private browsing and don’t want to have to log in every time I want to upvote someone.
The content is saved unless I explicitly reload or navigate away from the content. So I can close the app and come back to exactly where I was rather than the browser that will not save that state and then try to reload even if I don’t have an internet connection.
Navigation is easier in the app, because every action is clicking anywhere on the post and selecting an action from a large pop up menu. Except for collapsing/expanding which is also easier because you click the post header not just a tiny dash.
Automatic dark/light mode.
Etc. Etc. The app I use isn’t perfect but it’s preferable for lots of reasons to visiting the site directly.
I also only use private browsing mode, but the login annoyance is not enough to make me use an app. Most apps in fact track like crazy (potentially even third-party apps for sites like HN), and the whole point of private browsing is to not be tracked.
Instead I just lurk most of the time since I'm too lazy to log in, which means I'm not really contributing with votes. Maybe what we need to do is reduce the friction in logging in. I've always turned off the browser's password saving features and use my own password manager; maybe I should reconsider that policy.
[edit] Nevermind, apparently Firefox can't remember passwords when in permanent private browsing mode. So much for that idea :/
My only issue with the website is the little minimize "-" sign on comments is too small and difficult to reliably hit without zooming in. However as you say everything else works much more smoothly than any of the apps I've tried