Truama team should always have an rng change to show up when you kill a target. They should show up like the way they do on the prologue mission and give you an option boss encounter, either you back away and let them grab their patient or they attack you and you can attack them. They should be super hard but rewarding fights.
Such a missed opperunity for cdpr to not think of a creative way to implement Truama team.
This I think probably make a lot of "sensible" with the side jobs & gigs targets/characters that some of them clearly rich person or someone who could afford Trauma Team service. So, it would not be all targets but some that rich & well known enough.
Although, there comes a pickle of:
+ keeping target alive/incapacitated, trauma team arrived to retrieve target. If player died/incapacitated, the job actually failed, instead a death screen (load checkpoint/save game). Trauma Team arrival is immediate after you left the hostile area, so player have options to go loud or quiet or simply avoid them until "dump the body" to finish the job. This is probably much easier implemented in a scripted manner instead of randomizer.
+ killed a target. Now Trauma team arrived in this scenario wouldn't really make sense imo. It would be much better if a Special mercs arrived instead, trying to kill player no matter what. If player died/incapacitated, the job actually failed, instead a death screen (load checkpoint/save game). Special mercs arrival is immediate after you left the hostile area, so player have options to go loud or quiet or simply avoid them until "dump the body" to finish the job. Again, something like this feels much better in a scripted manner imo or things might go haywire pretty fast.
Basically, it would probably rather hard to implement with the jobs/gigs are basically on a different game design, but there are certainly a way to make Trauma Team a lot more prevalent in the game. Like limiting the options for this scenario happened on a much small number of exclusive/rich/powerful targets.