Think of the balancing and role-playing implications! In my opinion, they make paying Threat every time a deadly attack is made, very interesting!
If the PCs start the use of deadly force, they supply the GM with the necessary Threat to respond with deadly force, as well. Even more so, if there are more PCs than NPCs: Because the GM gains net-Threat in such an encounter, the advantage in numbers is balanced.
If the NPC start the use of deadly force, it’s up to the players whether they want to respond (and keep up the vicious circle of using deadly force). If they don’t, the GM will, eventually, run out of Threat. If this occurs, the NPC could, of course, still fire with weapons set to stun (eventually having to overcome the deadly trait of their weapons).
But if the NPC started using deadly force and run out of threat – then that is the perfect opportunity to reward the “Starfleet-y” behaviour of the PC and eventually de-escalate. Maybe the NPC retreat (since the use of violence did not work as intended) or they finally begin (or resume) to talk. Or they just change tactics and try to create disadvantages (which would, in turn, making threat-generation for more deadly force, more likely).
If not only the first escalation, but every use of deadly force generates/cost threat, you will have more dynamic encounters, I think. I think this reflects the pace of Star Trek shows very much and it’s very interesting that, mechanic-wise, “combat” doesn’t have to mean “combat until everybody’s down”.