Do you play tournaments often?
Par is VERY important when folks miss holes and the penalty is par+4. Depending on the skill level of the player, this matters quite a bit. Missing a Par 5 and carding a 9 is way different than missing a Par 3 and carding a 7 especially in your total score scenario.
I play tournaments fairly regularly and even run a sanctioned league. The scenario you cite above (missed holes) doesn't factor in because there's no pre-registration for rounds and thus, people are already there, everyone starts at the same time (since leagues are only one round), and everyone who's signed up knows where they're supposed to go. It's not impossible, I suppose, but you'd have to be a supreme idiot to have that affect you in a league.
Regardless, your point is well-taken...specifically for tournaments above L-Tier. I could see that problem arise here in Des Moines though, where some courses don't list have pars listed. (Ewing Park is an example of this.) In that instance I think the most fair way to do it would be to default to the "everything's a par three" mentality, in the absence of clear guidance.