Telegram blocks attempts like these by saying that doing that kind of stuff is against TOS. Then they can use that excuse to have apps taken down from the play store/app store.

To receive push notifications for iOS/Android apps, you need to upload your developer keys (!!!) to Telegram push server. So they can ban clients that disable advertising.

The open source fdroid builds don't do that, instead they receive notifications another way, without google's push service.

Can you please elaborate, what 'another way'?

I know only one: keeping the app running as a service, with all associated drawbacks. The app we develop (an XMPP client) does just that.

On iOS, it is not possible at all. To make an app receive messages and notify user about them, you must use APNS, and to do that you have to upload your keys to Telegram.

Yes, the app runs in the background. It kills the battery, but you have to compromise on that if you do not want to have google services on your phone.

Telegram users who want to avoid ads and people who want to keep their phones google free are two very different audiences, which shouldn't be conflated.

1. Too much of hassle for most people out there. 2. (hypothetical) desire to keep Telegram afloat? I would rather pay a recurring fee though than get ads, but if the choice would be "Telegram with ads" vs "No Telegram at all" (if they run out of money), I would prefer the former option.

Nothing, probably, but the vast majority of the 500m MAU all but certainly use the official client, rather than a homebrewed one.