We have extensively tested site speed, and taken a long hard look at UserNames, I can safely say that UserNames does not slow down your Site. The biggest bottle necks come from other places. 

Usernames is a fairly good module, it does need to be polished as it is lacking in a number of areas and the developer is not willing to improve, but the module works well and does what it is designed to do. Even with the feature failings in the module I would recommend purchasing Usernames and supporting this developer as it functionally does what it is designed to do.

Speeding up your site:

If you have any code in >Studio >Designer > injections take it out, your site will be so much faster.

https://your site.com/studio/designer.php?page=injections

Analytics and Advertising code can really impact on your sites performance, removing that code from the header and body will make your site fly.