I actually don't mind the time limits because it allows for several games in a day vs. that one match-up that gets dragged out due to high agility, high health, etc.
I'd say the "does it matter" question lies on what makes the game go to time. If it's because the rules are bloated and the time is spent figure out how the text of different cards interact with each other, then that's a problem, because it means games are going to time due to factors other than truly playing the game.
If it's a matter of playing a strong opponent where every move needs to be carefully thought out and executed, and you and your opponent are denying strong attacks against each other's valuable ships, it's not a problem. That's part of the game. Not every battle or war ends with one side entirely getting killed or blown up.
I've struggled up until recently about how tournaments require a different approach. Sure, it's my advantage to destroy my opponent's ships, but sometimes I know that's not going to be possible. So I have to plan accordingly.
Some cards and interactions can be complicated and it can take a lot of game time to ensure triggers are happening properly. But I've found most of my games that go to time have been because of excellent flying on both sides.
That all being said, I played in a hyperspace trial last weekend that was 5 rounds. Only one game got completed. Only one of the other four got remotely close to being "completed." I don't know if that's a bad thing or not, but just wanted to share the real-world experience.
Anyway. There's my two cents.