That's one of the biggest problems. The pilot obviously has a lot they can do with choosing where the vehicle goes, how fast it's going, maybe even being able to fire a weapon, etc., etc., but when you're a crewmember or a passenger there's typically not much for you to do. Rogue Trader from Fantasy Flight Games (based on Warhammer 40k) allowed multiple players to participate in ship-to-ship combat, but often there was only one thing for them to do every round. The priest in our group pretty much just rolled the same skill check every single round and was both tedious and repetitive.
I'd say that is the key problem, and this touches a little bit on why tactical skirmish combat is almost always the only effective core RPG play.
The problem is more specifically that though the characters who are not the "Master & Commander" of the vehicle often have a lot to do, the players of those characters do not. Except for whomever is in command, no player has any interesting choices to make. The character may have a lot of interesting choices to make in hectically routing and allocating power to systems, or bolstering and configuring shields, or performing damage control or whatever, but from the player's perspective (as you observed) they are just rolling a dice every round - often the same dice. When you aren't making choices, you don't have any agency and so above the age where the card game "War" is fun, you probably aren't having fun.
Now I've seen this problem solved in elegant ways in video games - most notably in 'Puzzle Pirates' and 'Lovers in a Dangerous Spacetime' - where every crew member has their own engaging, hectic, time constrained tasks to perform, but some aesthetics from real time video games are just difficult or impossible to port into a tabletop RPG. Without time constraints and sensation aesthetics, minigames created for specific crew tasks aren't likely to be engaging in the long run. They'll likely just be fiddly math to figure out the 'right' thing to do and a die roll to do it.
Maybe even worse, you run into the problem that cooperative board games often have, where in practice you rarely have real collective decision making and instead one dominant personality makes the decisions and is effectively playing all the characters. Afterall, whomever is making the tactical decisions about where to go probably is basing that decision on the expectation of certain resources being available and deployed in certain ways and certain actions being taken. And so once that decision is made, it's often strongly implied and heavily constrained as to what everyone else is going to do.
It turns out that tactical skirmish combat is "special". It has some properties that turn out to be almost unique and that trying to develop different pillars of gameplay is very hard or maybe impossible (in that nearly 50 years into tRPG game design no one has done it).
The only ways I've ever made vehicles remotely interesting is just make the vehicle effectively the platform on which tactical skirmish combat is conducted. For example, in my Star Wars campaign, the most commonly employed vehicle is a large open topped land speeder. One person drives while everyone else engages in what is effectively ordinary combat - typically against parties in other open land speeders. Only one person is controlling the vehicle, and he has the option to stick a pistol out the window (as it where) and engage in combat as well as control the craft, but everyone else is in a normal fight including the possibility of melee boarding actions. For an example of this being reasonably well done, see Season 2, Episode 7 of The Mandalorian ("The Believer") with the party engaged in combat on a rolling bomb.