How much does image optimization matter for website performance?
It depends on the website type, but images can make up to 80% percent of your content, and as such, can be crucial for optimization.
A great number of websites do not care about the image size, so some pages can be quite large (over 10MB even), which can be too much even for desktop users, and especially for the people browsing using cellular data. Image size and any other resource influence the IO process, spending server hard drive, and bandwidth itself.
Images need to be optimized as much as possible and kept in .jpeg format unless there is a need for a transparent background.
The alternative to standard formats are .webp, and .svg which help improve website speed and resource management.