Assuming a message is 200 bytes or so, searching millions of messages is trivially doable on your phone (200 MB full text index). Billions is pushing it a bit, but you can work around on the app level (e.g. only index the last month in high traffic groups).
How do you handle message history? Do you download every single old message to your device? Who hosts these messages? How are the backups handled?
This is patently false. Local indexing and search will always outperform a network call
How are you indexing literally billions of messages on tiny mobile devices? What happens when you wipe your device and you want to have your chat history from before? How do you download all the previous chat messages? Who hosts the chat index?
I think it is very unlikely for a conversation to reach billions of messages. There are less than 32 million seconds in a year. So, Yoigo would need to send a message per seconds for decades to reach a billion.
Of course there are people who are much more popular than me, so it might be possible and I am not aware of it. :)
These are channels and groups with thousands of members.
https://t.me/durovschat Has 9500 members
https://t.me/swhkdemocracy Has 6000 members
https://t.me/linux_group Has 6000 members
https://t.me/PublicTestGroup Has 18000 members
There is no limit to joining these chats. These design decisions Telegram has picked has allowed the app to be quasi social media, rather than just IM. You can't index these and maintain chat history locally. You'd need way more bandwidth and energy and computational power than the average cellphone has.
Telegram is used a lot in developing countries which are using phones made 3-7 years ago. Or phones that are made recently but with old chips and tech. Maintaining a search index across literally millions or billions (some groups are really really big) messages isn't something your phone can reasonably do.
I do wish telegram was e2ee for IMs, but for groups and super groups and channels I don't particularly care.