True philips head screws are designed to "cam out" when over torqued. They were originally designed for mass production as the head is self centering for machine power screw devices. If the machine torque is set too high, you get rounded out heads (screw destruction) instead of stripped threads in the host part resulting in destruction/damage much more difficult to repair "as new".
Lots of cross point screw heads are not true phillips design. There are variations on the design that have flat slots and tapered slots. Also, the bottom of the "V" can be pointed, crowned, or flat. The Angle of the "V" can also be different.
The Phillips was the first widely used cross point head widely distrubuted. Now, much like Kleenex, Xerox, Coke, etc. everything that looked similar got the layman's description of Phillips even though it may not be a true Phillips design. I've seen people use a No 1 Reed and Prince tipped screwdriver on a type 1 Number 2 sized cross point and then curse the screw when the head striped out!
Using the properly matched cross point driver tip to the screw being serviced will go a long way to keeping the screws functioning as intended.
The cross point design is self centering, but not self aligning. Angular misalignment greatly increases wear on both the screw head AND the driver tool. Wear is bad and reduces screw head performance. Misalignment also reduces the maximum torque transferance capability from driver to screw head. Part of the reason why impact drivers work so well is that angular alignment is often idealized due to the screw head being reformed by the impact process.
Finally, worn driver tips can destroy each and every screw head they are used on, even if properly matched to type.
Always have a brand new driver on hand. Take a look at the tip's edges with a magnifying glass. If the edges aren't sharp and well defined compared to the new one, it's worn! Worn tips will improve the chances of cam out and usually deform the crosspoint head in the process.
I know, it's difficult to give up that favorite screw driver that has been your friend for many experiences. I suggest a quiet and reverent funeral service just before the heave into the trash can. You are more likely to enjoy life at least a little more with a brand new driver in your hand flailin' on screws.
Cheers,