As far as I understand the international police is fighting against money laundering with crypto now. That's why all mixers are under high pressure.
To be honest, if you want to use an exchange platform to mix your coins better to make waves with your tshirt with your name printed on it. Your solution is one of the last I would do. It's so easy to track people. And if people say it works fine then they think it works because they didn't get any problem, but does it mean the solution is correct? No. Because you don't see the SWAT at your door tomorrow for the coin you mixed 2 days ago doesn't mean you mixed your coins correctly
Use proper mixers to get proper results or you will get what you pay for
+1 on this. Mixing your coins in an exchange can easily be tracked.
imo this can even cost you fee much more.
If you need a mixer just use a real mixing site.
There is cryptomixer which I personally used before and had no problem with using it.
Their ann: https://bitcointalksearch.org/topic/m.14956325
Chipmixer, this one is actually a really good mixing site. I've only used them once but they are different to other normal mixer.
Another one is Bitcloack. Again, I have only used this once and everything went smoothly. The owner of this site is not that active here in bitcointalk or in advertising his mixing site tho.
All of those three have an onion link btw. You can use that instead of the clearnet version for extra anonymity.