It actually saves at least 4 bytes per closing tag. On a larger webpage, that could easily add up to saving hundreds or thousands of bytes per request. That's a significant savings, especially for mobile.
I just took a sample page out of here which has bunch of p tags open and closed, gzipped the original and the one with </p> stripped, difference was 39 bytes.
Ironically, if end tags were truly non-optional, html might actually compress better, because it would have less entropy (less choices). In practice, it would allow for a compression filter to represent the tree structure in a less redundant form with fewer corner cases to deal with (much like compressors do for binaries, for example).
I just took a sample page out of here which has bunch of p tags open and closed, gzipped the original and the one with </p> stripped, difference was 39 bytes.
https://en.wikipedia.org/wiki/C_(programming_language)