Eh, web traffic can be measured too. App installs aren't all that interesting if people install the app and never use it. Therefore, valuation metrics should be driven by usage (regardless of platform).
I think companies want you to install their app for a couple reasons:
- Sunk cost - I would guess people feel a lot more invested in a service after installing an app (and then being forced to make an account, in many cases)
- Mind share - Their logo will appear in your app drawer and they will be able to send you push notifications
It must be effective, because many companies push heavily for app installs. Check out mobile reddit, for instance. Although yes, I think that a lot of this is useless metric driven strategy.
You forgot the most important reason: telemetry. An app can exfiltrate an order of magnitude more kinds of interesting data on you than a webpage ever could.
And the second most important reason: push notifications.
A big reason many companies push for app installs is because it gets them out if the business of having to pay a very high Google tax for traffic. If a hotel company can convince you to download their app, the hope is that the next time you search for a hotel you go straight to their app, instead of going to Google where the hotel chain would have to pay out the nose for very competitive AdWords.