I just finished making a social application (for skateboarding) with the express intent of making it fully featured/pleasant to use on mobile simply as web app, without login or installation.
Web is such a powerful platform and so many people still treat their web applications like they're just interactive documents. I think the most bothersome thing on mobile web is if an application has shifting framing ("chrome") when you pan around, like you're looking at a PDF.
Let me know, but I developed it almost entirely focused on iPhone SE as a target to give myself the most claustrophobic possible experience, and I think that helped guide a lot of the decisions.