I think it's super cool to be able to interact with different people doing interesting things (a little like HN, but it's easier to remember who the people are where as on HN I never remember 99% of the usernames in threads).
If you want to be extreme about it, you can put everyone in lists and then this won't happen. You can also use a third party client that doesn't do this.
My main Twitter complaint is the ads. There are so many and they suck. I'd much rather have Twitter premium that removes the ads.
There are no ads in third party clients such as Tweetbot.
Are you using the reverse chronological timeline? That's the only way to fly.