Could a higher number of registered image sizes affect performance?

Depends. One argument could be that if the requested page use all sizes then there will be a lot of image calls (slower response, bandwidth etc) but you can bypass that i.e. by loading images with JS. Also more sizes means more disk space usage. I don’t think there is any significant performance concern related to back-end, meaning the db calls / queries etc.

Also if the images are compressed from the begging a few pixels down in width or height won’t be a difference in performance.

You can have an image with 600×900 dimension and cover a lot of intermediate sizes adjusting with CSS and keep a good aspect ratio and have a good quality for retina monitors. Better to have a bigger, in dimension, image and shrink it than to have a smaller image and scale it up.