In the US, you shouldn't shoot to your handicap 75% of the time either at home or away. Remember it is the average of your 10 best scores out of 20. To say that 75% of handicaps don't travel well seems to be obvious for that reason to me.
If you are playing a course where the course rating is higher than the par, you should should your handicap (vs par) even less frequently. This is because handicap is based on the course rating, not the par.
In "legitimate" tournament play, the only bottom line is what the total number of strokes was (or how the match came out.) Par means as little as handicap.
In my mind, Par is the more irrelevant number as it really should have no effect on any part of the game. Either in gross or net play.
By the way, as long as Rule 6-2 exists, I would dispute your statement that handicaps are irrelevant in legitimate tournament play.