Transverse jump doesn't actually help you escape fleets. You have to be fast enough to open up a gap to use it, so you also must be fast enough to run away conventionally. It does save you a lot of time over slowly running away with a +1 burn advantage, and maybe saves you supplies if you would have to eburn to escape and don't have the skill that makes e burn free.
The only thing it does that actually can't be done otherwise is avoid jump points, particularly in remnant system where jump points are very dangerous. That's definitely nice, but not game breaking. In general it's mostly a time saver/qol that I value very highly, but it doesn't actually let you do very much that you couldn't do slower, or with other abilities.