Making things only available in the mobile app version of a service isn't just a Google thing. You can't even mark/unmark an Instagram account as a "Favorite" in a browser.
BUT, I have to say, there is at least some small bit of reasoning behind making the Timeline only work in the mobile app, since that's what you would be using when you actually go places with Maps. A very small bit of reasoning, I say. Obviously it's useful on a desktop if you consider what many users would want to do with the Timeline, like documenting trips. Also, it doesn't let you have a consolidated history from all devices.
In actual fact the reason it doesn't work in web browsers now is because they decided to store the history on your device rather than in your account. The big reason for that is privacy; authorities can't subpoena/request your location history if Google doesn't actually have that history. So, I don't know if this is a "fuck you Google" situation since they are actually looking out for us in this instance, or at least looking out for themselves by avoiding any controversy by making it impossible for them to comply with requests, and it happens to be very good for us as well.
Don't forget, Google also likes to fuck Linux and other OS users in the ear if they take away a feature from the browser version of a service.
It's odd that the website
https://www.google.com/maps/timeline still seems to be functional, and acts like it WOULD work, but I have location history disabled anyway so I can't tell what it would actually show. Also weird that you can turn if on and off in your account in the browser even though it only functions on the device.