My current character has Adrenal Defense, so not parrying is not such a big deal. A large part of his total OB-DB is mandatory DB anyway.
It depends a lot on the kind of situation you find yourself in. In our last session, we were fighting a demon-possessed troll (I think), and we ended up with at least one person doing full parry and drawing its attacks, while a second person full attacked. That was an option because the GM decided it didn't want to face the direction the Beacon spell was coming from. It's DB and AT were high enough that, aside from the fighter, none of us could touch it without full attack, open-ended rolls, or both. (The combat lasted 43 rounds! Including a short break where we let a large group of low-level archers try to drop it. They failed utterly.)
If you are in a regular fight where you have the OB advantage, it makes sense to parry enough that the opponent needs to open-end to crit you, and preserve your ability to hit them with a regular roll. That depends on how much they parry as well, so you have to gauge their behavior, too.
If you are at a disadvantage but support is on the way, it makes sense to parry to buy time. It slows down your melee. If support is not on the way... hard to say. You should probably try to escape.
It actually doesn't matter who is doing the parrying, you or your opponent, just the total amount of parrying going on. So even if the players never parry, the GM can compensate by making the opponents parry a lot. If neither side parries, combats will be quicker...
When I read this thread title, it made me think it was the title of a story. Probably with a subheading: "We never parried: Tales of a TPK."