The reason why I decided to make VATS off-limits when one of the player's arms are broken is that using VATS allows the user to pretty much nullify the effects of having a broken arm, since gun sway doesn't factor in.
VATS has broken-arm penalties, where your chance of hitting is dramatically reduced. Personally, I've found that using VATS with a crippled limb is usually a death sentence because I don't hit much and then just stand there afterward soaking up bullets while the cinematic camera camera finishes doing its thing. I've played a fair amount both with VATS and with bullet-time, and find bullet-time to be a much more viable option than VATS when an arm is crippled.
This of course assumes that VATS is fixed from vanilla, since in vanilla FO3 it was pretty much god-mode, where you only took 10% damage. And if I recall correctly, your mod fixes that.
That said, I like having the fixed VATS available, and don't find it any more immersion-breaking than bullet time, since in real life I can neither stop time nor slow it down. And for me, the immersion in FO3 doesn't come from gunfights, which are (and should be) unrealistic for a number of reasons. The immersion comes from exploration and interacting with the environment, from needing to make smart decisions to survive, and from watching my character progress from an unskilled newbie to badass of the wasteland. Vanilla FO3 really left out those last couple things, and your mod adds them in beautifully.