@mastertrader_, just being curious, what made you use their service among other very good and reputable ones?
I saw an advertisement for this service on one of the crypto-related websites I visit. They promised an exchange without registration or KYC so I decided to give it a try by swapping a small amount first. I also can admit that I was allured by good exchange rate they promised so I forgot about safety for a moment

As far as I know, Bestchange is not against transaction stops and KYC procedures when it comes to "dirty" coins. I think a crypto exchange service have a right to refuse participating in laundering coins that were involved in illegal activity by informing their customers about it beforehand. Bestchange faq says the following about it:
Although the exchangers listed on BestChange do not always have a special icon indicating the necessity of verification, they all are obliged to comply with AML&KYC requirements, according to which they may request a set of documents from a customer, shall their transaction be marked as suspicious. It is recommended to study the terms and conditions of the selected exchanger carefully. AML&KYC policy complies with international practices for anti-money laundering and countering the financing of terrorism. The exchangers listed on BestChange use these procedures to align with AML&KYC requirements but not to abuse customers' data or arrogate their funds.
For more information on AML regulation, please see the AML FAQ section.
I checked quickex, they have AML policy posted on their website so it's no wonder they block transactions if the risk level is too high. The question is, do they return coins after their customer passes KYC or not

Have some of you tested how they conduct KYC procedures? I'm curious.
I myself always keep an eye on the risk percentage of the coins I have in my wallet before I send them to a service that have information about AML or KYC posted on their website. I get my coins legally, I think I have nothing to worry about. I am not against KYC in general, but it is something that I don't want to happen to me for several reasons. To be honest, I have never had my coins blocked by a swapping service before (probably I'm lucky

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I also checked their topic briefly and that's what I found:
We don't block transactions and request KYC on our decision.
Since we work with liquidity of our partners, they can stop transactions in case they detect high risk factors. In such cases, they request KYC. Here, we also work as a middleman and help our clients prepare all necessary documents to pass the KYC successfully. All our AML officers are certified and work according to the Privacy Policy. We also provide a free risk score checking option. We guarantee 100% KYC-free exchange in case our client passes this check successfully.
This explanation seems reasonable to me, at least they are being honest. Probably I'll check their "risk score checking option" sometimes and see what comes out of it.