I have personally gone through coinmama, of a horrible wallet confirmation prior with my kyc requirements only to still wait for a response.
I wouldn't recommend coinmama to anyone. Their privacy policy gives them
carte blanche to share your data with pretty much anyone they like (emphasis mine):
We may share Personal Information with the following recipients: (i) our subsidiaries; (ii) affiliated companies; (iii) subcontractors and other third-party service providers; (iv) auditors or advisers of our business processes; and (v) any potential purchasers or investors in the Company.
In addition to the purposes listed in this Privacy Policy, we may share Personal Information with our recipients for any of the following purposes: (i) storing or processing Personal Information on our behalf (e.g., cloud computing service providers); (ii) processing such information to assist us with our business operations; (iii) performing research, technical diagnostics, personalization and analytics; and (iv) communicating promotional and informational materials, in accordance with our marketing policy (see below under "Marketing").
"Performing research, personalization, and analytics" is a fancy way to saying data mining and surveillance companies. Once such companies have your data, how many places and how many people it eventually ends up with is anybody's guess.
The best alternatively to crappy centralized exchanges like Coinbase, and the best alternative to keeping your private information safe, is to use a DEX such as Bisq or LocalCryptos.