For each image size, WordPress creates unique image on image upload. Than, when you register 7 image sizes, and upload single image, 8 unique images will appear in your wp-content/uploads directory. Is this too much for small blog with 100 posts to have 800 images on the server? But having 1000 posts? It depends.
Another point of view - page load speed. When displaying another page of your site, seeing the same image but in new different size (thus no cached in my browser), I have to download that image again and that makes page loading slower and user experience poorer.
When you remove default sizes, I guess that after chaning theme from yours super cool one to another even more super cool one, user will have to recreate all thumbnials in order to have thumbnails on default size available again. This might not be an issue, there are plugins for that, but again, when having 1000 images on my site, this task would be really resource demanding.