There are people that use Bitcoin mixer to cover the origin of there Bitcoins with a veil.

I will never make this, because this would make my BTC suspect. And there is a risk to make my BTC's dirty.

But here is my technical question:
When we change our BTC into another crypto and after change them back into BTC, I guess in this case it would no more be possible to trace back the origin of the  origin BTC.
Am I right? Or do I miss anything?
Of course if we make the change on a CEX, it would be possible to trace back the origin, because the CEX will have a history-protocol. But I guess not, when we make this via DEX.


If I am right: Why do people use BTC mixer? Isn't changing BTC into another crypto and change them back, not the much better solution to cut off the trace?

Would appreciate a competent answer. Thank you.