and unfortunately, the way damage scales in Shadowrun, anything powerful enough to punch through military armor will also likely be powerful enough to outright kill the character
On the subject of escalation. The real danger isn't necessarily killing the problem PC. Many GMs have a tendency to adapt to a group's strengths in order to challenge them better. It's an easy mistake to make in Shadowrun to up the firepower on the badguys in various ways and geek all the glass cannons that are the rest of the Shadowrunner group.
And yes, if you do simply kill the PC, or take the armor or whatever gizmo, you risk your reputation among your players being ruined. The players are already aware that you can do whatever you want to their characters and reminding them of this forcefully does not instill trust in you as a GM. Talking to the player or showing how the armor is a disadvantage in the SR world are better alternatives. Limiting availability is another "soft" option, as opposed to options that involve forcefully neutering the character in various ways.
There are good reasons to take items away from players, but this should not be confused with GM stealing items to maintain play balance. It's a whole other thing and it relies on group play styles and tastes. One, the GM might steal an item as a way to set off a series of adventures. It's a great way to make a player very interested in the outcome of the game if their item is at stake. Two, it's a great way to paint the gritty nature of the world to have master thieves out there who boost and sell high end gear. This second option in particular is heavily based on the tastes of your players though. Many players out there are of the school of thought that their gear should never be taken and you really need to know what kind of players you have before attempting this kind of thing.
It's all about your motives for taking the item, because the players will certainly know why you're doing it if you are doing it to neuter a powerful character.