I think the rules were built for the various skill bonuses characters can trivially get, but that wasn't mentioned anywhere. Mystics get a +7 to Connection skills, Mechanics get +6 to Computers and Engineering, Envoys get 1d6+4 to skills of their choice from a list and you've also got item bonuses... There's lots of bonuses.
Lol, not even that.
Let's be a 15th-level party, with a 15th-level starship - your upgraded Millenium Falcon style Explorer. Though it doesn't matter what kind of starship it is really, unless you get massive crew-bonuses (more on those later).
You want to do an Evade-maneuver, or your Science Officer wants to balance the shields, or basic stuff like that. The DC for that? DC 45
Gods forbid you're a captain who wants to give Orders to give crew members additional actions, or and Engineer who wants to overpower one of it's systems, because those have a DC of 60.
So you're 15th level and up against a DC of 45.
You obviously get 15 ranks from your skill, and 3 from being trained in it. That leaves 27 points you have to get somehow.
You can get +4 from being the right class, at this level. - an Engineer for Engineering or Science, an Envoy for Captaining, a Technomancer for Science, or a Mystic or Operative for anything. 23 to go.
You start with a 17 or 18 in the relevant score, increae it three times to 20, and then add a MK 3 Personal Upgrade to it to go to 26. That's a +8 bonus - 15 points to go.
You'd think you could take Skill Focus to go further, but it's an Insight bonus - so it doesn't stack with any of the bonuses you get from your class.
So that's that. To perform a
basic starship action, a
really specialized character only has a 25% chance of success.
Fortunately, I left something out - Starship computers can add a significant bonus to that. If you sink a fifth of the build points you get at this level into your computer, you can give two people a +7 bonus to their check. That puts them from a 25% chance of success to a 65% chance - so you'll still fail a third of the time.
And of course, the computer can only grant it's bonus to two people at once. So if you have a captain, a science officer, an engineer and a pilot - better pick which two of those have a reasonable chance of success.
Okay, one last thing - your Captain can also Encourage people, giving a +2 bonus. That's reasonably doable, with a DC 10 in the skill they are using or a DC 30 (at 15th level) in Diplomacy.
They could even try to make a Demand of them, using Intimidate, but that'd be right up to DC 45 so good luck.
This of course means that the Captain is in a ton of cases just relegated to providing minor bonuses, which I imagine becomes boring really quickly.
Oh, and none of this touched on the DC (15+ Tier x3) checks. Because even with computer assistance and maximized build and a succesful demand from your captain, good luck making a DC 60 check - all the bonuses add up to +41, so you have a 10% chance of success.
Of course, you then add +2 to the DC of all checks at level 16, while only getting another +1 bonus. At level 20, you'll have gotten +2 from your class source, maybe +1 from an attribute increase, and the very best starship computer ever adds another +3 (and eats as much build points as a dreadnought chassis).
Your DCs went up to 55 - a 10-point increase, while your bonuses increased by +6 (with the computer that is). Your chance of succeeding at anything have actually dropped, down to nothing without computer assistance (even a 20 wouldn't be enough unless it's an auto-success), a 30% chance with computer assistance, and a 40% chance with computer and captains assistance.
A hard task now has DC 75. Zero chance of success even if you focus everything on it.
So I mentioned crew bonuses.
Obviously, you don't get those in tiny, small, medium or even most of the time with Large ships. And everything larger is supposed to be for NPCs (it states so on p. 305 under "upgrading systems", it needs GM-discretion).
But even then, there's no actual rules for that crew assisting you. Can you use Aid Another? In that case, just assign 5 crewmembers for a simple +5 bonus, in which case big starships reign supreme. If you can't, there's no framework at all.
Bottom line:
Even a very optimized character does, at higher levels, only have a worse-than-even chance of actually doing anything during each starship combat round.
Unoptimized characters have no chance at all - want to be a combat engineer who doesn't pump Intelligence as much as possible? Good luck doing even the most basic starship tasks at higher levels. Nevermind a class that doesn't get a scaling skill bonus - those can keep up for a while with skill focus (which gives +3), but at high levels they're just out of luck. At least you can always be a gunner.
But it gets worse than forcing players to utterly optimize and then still failing a lot. Eventually, you just need your starship computers assistance - but only two people can get that at most, ever. Which means the main tactical decision each round is "which role do we actually need this round", and I guess everyone else spends a round doing nothing.
And let's not forget how things are utterly disfunctional for the checks that scale at tier x3, because eventually it's just impossible to do those anymore.
It's just utterly baffling how any supposedly-experienced game designer could think that a DC that scales faster than your level increases was a good idea. The Truenamer had that exact same problem and is infamous for it for a reason. The only somewhat-reasonable design goal I can think of is to force players into lower-tier starships than they could afford, but in that case why not just adjust the tier you can afford? And even then it'd still force hyper-optimization and utter specialization just to keep up.