Aren't transactions id-s compromising privacy?

self.Monero1m ago
I first thought that Monero is completely anonymous, but actually there can be some scenarios when tx id-s are pretty much giving away privacy. Let's say you buy XMR on Exchange1 and withdraw it to your own wallet. Then you send your XMR to Exchange 2 from your wallet. Exchange2 can see 10 signatures/tx id-s that possibly belong to you, and those 10 signatures lead to another 100 tx id-s, and from one of those 1 belongs to Exchange 1. So if Exchange1 and Exchange2 are colluding together, and they suspect that you're the same person, they can actually figure it out that from those 100 tx id-s which one originated from Exchange1 so there's a high probability that you're the same entity, which compromises your privacy. I think it would be way better if there wouldn't be transaction signatures at all, because even if there are 10 decoys and 1 real, it still gives away some info, which can be used for probabilistic analysis. Alternatively signatures should be encrypted in a way that it's impossible to associate them with previous outputs.