well yeah, but a local app can get a more detailed fingerprint off the user, which includes location visited, app installed, habits etc. an app can do a lot more things when installed and closed compared to a closed browser tab.
> the Yelp app I don't get any ads
the profile is sent upstream and aggregated. ads served from other apps and on web pages you visit have a chance of using information collected by yelp even if yelp itself is not showing the ads, that's the point of it, a seemingly innocuous "ads free" app collects telemetry and third parties use that info to build a profile and serve personalized ads on other apps and web pages, correlating sidechannel info (last seen position, ip and other) to unmask your browser/app session and pin it to your "shadow identity" in the advertisers' system.
Or to put it another way, Yelp would be rightfully lambasted for not having a mobile app. Having a mobile app is table stakes for a site like Yelp. And if you've got all this engineering effort going towards a mobile app, why double your workload by also building a first-class mobile site? The mobile site just needs to be functional enough to satisfy the basic needs of casual users.