Images that are too big take too long to load.
That’s it in a nutshell.
Your site will load slowly because of the images.
Google cares about how fast your site loads and slow pages won’t rank very well.
This is one of those things that may be holding your site back without you ever knowing about it.
Another reason why you should care is because of the amount of bandwidth your site uses.
Bandwidth usage today is far less of a concern than what it once was.
The reason for that is that bandwidth is now much cheaper than it used to be.
Though, if you have a high traffic site, not optimizing your images will cost you quite a bit of money in overage charges.