How do I change how images are aligned (WYSIWYG Editor)

I’ve used WordPress for some time now and have noticed something: Images needed the classes “aligncenter” or “alignleft” or “alignright” or “alignnone” to be aligned (or not aligned). But there’s a problem with this: If I were to link my image to some URL and that same image has the class “aligncenter” (because it’s treated as a block), it causes the whole block of space it occupies to also be linked.

What I want to know (or know where to find the data for it) is if you can change it so that instead of adding alignright/center/left that it wraps it around <p class=”aligncenter/right/left”></p> tags.