And Twitter doesn't really care how you feel about that. They use your timeline to try to make the ads they show you relevant, so they don't want you getting rid of them. If you want to delete them on Twitter, you have to do it one at a time. They even say in their own documentation that if you want to get rid of all of them without changing your user name, you should create a second account, delete your account, and change the name of the new one to your old one.
Of course they don't mention that you'll have to re-follow everyone and all those people will have to re-follow you. Quite an undertaking.
I looked into mass delete utilities and found TweetDelete, which lets you delete 3,200 for free, which I realized after my first batch. I ended up buying a month of premium service with TweetEraser because I didn't notice that TweetDelete does a lifetime premium account for a few dollars more. Oh well.
After a couple of batches with TweetEraser I thought my Twitter account was messed up because Twitter said I still had 22,800 tweets but it wasn't displaying them and TweetEraser couldn't find them. It displayed about 400 on my Media Tweets tab, though. I tweeted at Twitter about it but of course they don't answer, and they have a help page where you can open a ticket, but once it's complete you get a message that they can't respond to individual issues, but they use the tickets to improve Twitter overall. Kinda misleading.
Anyway, someone at TweetEraser saw that and reached out, and explained how I could use a twitter export and upload it to their site to have control over what I wanted to delete even though it wasn't displaying correctly. Turns out I'd already requested a twitter export before I started working on all this just in case, so I uploaded that and then asked it to delete everything. That worked great and now Twitter says I have 29 tweets, which is correct or close to it.
And I set up a recurring job on TweetDelete that run every few days and delete my tweets that are more than a month old. It'll be interesting to see if I can warm up to twitter more again if it's a communication device and not an archive. I used to use it a lot more.