I think all y'all talking about how to destroy jump gates/destabilize jump points/whatever are going about it wrong.
Steve has already said he doesn't care about plausibility, since plausibility can be supplied with a technobabble explanation regardless of whether jump gates are permanent or not. Rather, if you want jump gates to be destructible, you need to demonstrate how that will enrich the strategic layer of the game, rather than diminish it.
Right now, setting aside NPR silliness that will change in C#, the creation of a jump gate is a real strategic decision. On the one hand you immensely simplify your internal logistics. On the other hand, you make yourself more vulnerable to strategic outflanking and enemy attack. Each jump gate you make is a decision that should be carefully considered.
If jump gates can be destroyed, that changes. Can we change it for the better instead of just taking away player agency? If so, then maybe jump gates should be destructible. Otherwise, they should stay permanent.
Don't worry about the how; focus on the why.
Myself, I think a cool system might be required jump-gate maintenance. Each jump gate you construct requires both an initial mineral investment and some small but not inconsiderable annual upkeep. Further, jump gates come in different sizes, with larger sizes being unlocked by research and requiring correspondingly higher maintenance. You can choose to forego maintenance, but the gate will degrade and eventually cease to function on some time-scale to be determined, possibly with chance for bad effects if someone tries to transit a partially functional but unmaintained gate.
This opens the strategic decision to use jump gates from being a one-time thing to being ongoing, and still definitiely involves strategic trade-offs for simplified logistics, as well as not simply allowing the player to remove inconvenient jump-gates immediately (but nevertheless involving risk to invading forces using an empire's jump gates). Alternatively, you could be able to blow up or deconstruct jump gates instead of just waiting for them to decay, if that's desired. In either case, if you desired a jump-gate on that point again, you'd have to pay the initial construction cost again.
If this idea were implemented, I'd like for minerals to be magically removed from stockpiles for maintenance, much like ships that are in orbit and using maintenance facilities. Colonies could have a toggle called something like "Maintain in-system jump gates", and then the capital colony (or, perhaps, a player-designated colony) would be responsible for maintenance on all other jump-gates. Any gate maintained by a given colony should be togglable so that maintenance can be abandoned, much like how we can stop and restart a colony's industries.This would vastly simplify the logistical overhead of jump gate maintenance - otherwise I'd probably just deploy mobile gates aka commercial jump tenders instead of bothering with all the faff.
NPRs would use the same system. In event that multiple empires have colonies in the same system, you'd be able to see which jump gates some other empire is maintaining before choosing which you will maintain, with priority being given to whoever decided to maintain it first. This way you could mooch off another empire, at the expense of not controlling maintenance. Or, simpler, jump gates could track whoever built them, and the only empire capable of maintenance on that gate is the empire which originally built it. If you want to maintain it yourself, you have to wait for it to degrade (or destroy it, if that's an option) and build one yourself.
Precursor gates, on the other hand, should not be subject to maintenance and should probably be permanent - they're made of super-hard unobtanium-neutronium alloys and partially sunk into the liquid dimension, or something.