Phillips bits are notorious for two failings:
Unless you use an “anti-cam” tip, Phillips tips will cam-out under extreme torque. Snap-On tools used to sell ACI and ACR (Anti-Cam Insertion and Anti-Cam Removal) tip options on their Phillips screw driver shanks. I’m not sure where they are with that tip offering lately, but they used to be a life saver for getting out stubborn Phillips screws.
This tendency for cam-out is why you will see MANY stripped phillips head screws in a variety of places. Reed and Prince, and Pozi-Drive Screws were an attempt to address this issue, but without widespread uptake in the manufacturing community. Gunsmiths are so wary of cam-out resulting in firearm finish damage, that they have come up with “screw jacks” to try to deal with this shortcoming of the Phillips fastener type.
Under extremes of torque, Phillips tips, like many other tip profiles, are subject to fracture, damaging the tool being used. The root cause being that Phillips tip profiles just don’t have the same load distributing surfaces in play as you would find in a Torx, Penta Lobe, or splined fastener to driver interface; and Phillips fasteners just are not what you can call precision-made devices–one or two of those 4 contacting surfaces is going to bear more of the load than the others.
Putting a Phillips tip on a “T-handle” driver is probably seen as counterproductive, and may be avoided for the above reasons.