Which part of "it isn't designed to offer privacy" don't you understand? Of course and you can make an account anonymously, but that isn't my point. Your coins could be confiscated for either being "tainted", or your account could be terminated for using a "banned IP address". Can you gain privacy from such service? Perhaps. Is it suitable for that purpose? No.
The mixer you advertise is also not designed to offer privacy. How do you not understand that? Your mixer says it can confiscate your coins or terminate your account, so the only difference between using an exchange and using your mixer is that exchanges have a larger user base. It is not suitable for the purpose of gaining privacy.
The real question is why would you ever want to do that? The exchange isn't portraying itself as a mixer, and if you take the time to read their privacy policy, you'll quickly figure out that you have no privacy.
Did you take the time to read the privacy policy of the mixer you are using?
]3. Quality scoring of incoming transactions
We run a thorough background check of incoming funds through a proprietary algorithm.
]2.1. Privacy Policy
Please refer to our Privacy Policy to get an understanding of our confidentiality obligations. You consent to the collection and use of information as described in the Privacy Policy.
2.2 Suspension or termination of services
[banned mixer] reserves the right to suspend or terminate access to services at any time at its own discretion, with or without reasons, with or without notification assuming no responsibility whatsoever.
For example, services may be suspended or terminated due to the following reasons:
an actual or suspected violation of these Terms and Conditions;
use of the service in such a manner that is conducive to the legal liability of [banned mixer] or Service malfunction;
planned or unplanned maintenance, etc.
2.3 Unacceptable use
You agree that you personally will not commit, encourage or support the committal of:
use of any unauthorized means to access the [banned mixer] service or use of any automated process or service (for example, spider, crawler or periodic caching of information stored or generated by [banned mixer]) except for the functions described in our API, as well as distribution of instructions, software or tools with this aim in view;
modification, change, distortion or any other interference in work of the [banned mixer] service;
disturbing or interference in operation of servers or networks used by [banned mixer] to deliver the Services;
disabling, overload or degradation of [banned mixer] performance (or any other network connected to the service);
use of the [banned mixer] service or website for any other purposes other than those specifically provided by these Terms and Privacy Policy;
any illegal or fraudulent activity, as well as use of this Service in order to legalize illegal income, financing of terrorism, participation in schemes of phishing, forgery or other such falsification or manipulation;
unauthorized spamming, pyramid schemes or any other activity duplicating unwanted messages should they be commercially oriented or of other nature.
2.4 Service updates
At any time and at its absolute discretion [banned mixer] can carry out unscheduled works related to the service modification, update and enhancement. We are liable to add or remove functions and cease activities of the service and website.
2.5 License and restrictions
[banned mixer] provides you with a personal nontransferable nonexclusive license to use the Service as it is stipulated for you by [banned mixer]. This license is provided under conditions and restricted to the provisions, stipulations and constraints stated in these Terms. Therewith, such license is intended for personal, noncommercial use. You may not copy, modify, create a derivative work of, decompile or otherwise attempt to extract the source code of the service or any part thereof, exclusive of data permitted by law, or expressly allowed by the [banned mixer] platform (use of templates, API, etc.). You may not reassign (or grant a sublicense of) your rights to use the service, or otherwise transfer any part of your rights in accordance with these Terms. These Rules do not provide you with any license or permission to copy, distribute, change or otherwise use any applications programming interface despite any provisions to the contrary. No property rights or ownership rights related to the Service are not granted to you according to these Terms. [banned mixer] reserves all rights that have not been expressly granted.
This is why you should absolutely not be recommending mixers to the OP as an alternative for exchanges. You are trading one trusted custodian for another without solving the issue of privacy.