I think it would be already a lot more interesting if the Jump gates were usable by everyone, not just the owner. That way having the gates actually becomes a dual edged sword instead of just a pure win. This means they are actually conceptually different from jump bridges besides just being a superior version (except for jumping capitals). This makes the downside of not having jump fatigue the fact that also your opponents can use your shortcuts.
Just get rid of the fuel cost per ship jumped and introduce a (significant) constant fuel usage. Allow capitals to jump or not, I don’t particularly care.
I have explained in this topic in more detail why the current implementation of the ansiblex jump gates is a mistake: Ansiblex jump gates are a mistake