If it were me I'd put it more like:
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Threw Mario in because why not.
I would say Cloud is easily more well known/recognisable for multiple reasons:
-Final Fantasy is a much better selling franchise than Street Fighter, and Cloud is the biggest icon of the franchise even if he isn't the star of every game.
-Final Fantasy is immensely popular with the casual audience in the West, as is Kingdom Hearts (can't forget he's there too). Street Fighter is popular enough but it's popularity has definitely waned in recent years, because outside of Japan, fighting games have become increasingly niche due to the lack of arcades in the West and because people tend to favour games with accessible controls these days (of course, JRPGs aren't as popular as they used to be, but Final Fantasy hasn't really been effected by this).
-Cloud's presence in Kingdom Hearts should not be understated - it means he reaches Disney fans, which are a huge demographic. Kingdom Hearts: Union Cross (the mobile game) in particular is immensely popular and Cloud has multiple obtainable medals in his image in that game (and with more to come). Final Fantasy also has multiple immensely popular mobile games that Cloud makes an appearance in.
-Cloud is heavily merchandised, way more than Ryu is. There's way more figures, plushies, posters, etc, of Cloud than there is of Ryu, which I think is probably one of the biggest factors in how iconic a character is (the term "icon" in this context literally refers to the character being a recognisable symbol of a brand, so having lots of merchandise is obviously a big factor). Again, it helps that he's in Kingdom Hearts, since he gets plenty of merchandise based on that franchise too.
-Cloud has multiple designs, yet people always recognise him since his general appearance is unmistakable. Ryu is actually sometimes confused with other characters that have a similar design.