Tim Allen's character is shown to have a house in the Hollywood Hills, which would seem to indicate he's worth millions. Yet he's supposed to be a washed up actor who hasn't had a decent job in 20 years.
The other actors don't appear to be doing too bad either, yet they're so hard up for cash they're making appearances at electronic store openings.
There is no law that only poor people try to become actors.
For example, Tori Spelling (b. 1973) is an actress with some success. https://www.imdb.com/name/nm0001760/?ref_=fn_al_nm_1 But it is logical to assume that the majority of her present wealth comes from inheritance from her wealthy father Aaron Spelling (d. 2009).
And I don't think that an actor needs to have a super wealthy father like Aaron Spelling to inherit significant amounts of money from. A father or other ancestor who made a comparatively small fortune of a few million dollars and had only a few heirs to leave it to could have left enough money for an actor to live a rather upper middle class lifestyle even without his acting earnings.
Two:
Possibly the character has another career beside acting. Possibly he went to college and got a degree in a profession that pays fairly well, and acting was a minor part of his career until he got his first big role and he quit his day job. And possibly after his acting career stalled, he brushed up his knowledge of his original profession and got hired again and now makes a good regular salary. Or maybe he did until he retired last year, and now has a lot of free time to appear in conventions.
Actor Tom Tryon (1926-1991) became a star but retired from acting in 1969, and wrote a number of novels. I have read his novel The Other (1971) and seen the 1972 movie based on it.
Three:
It is a tradition in movies and television to depict characters living a nicer and more expensive lifestyle than they probably could afford to. Since Galaxy Quest is a science ficiton movie, assume that it happens in an alternate universe where for some unstated reason houses in the Hollywood Hills are more affordable.
I had other issues with that setup, besides the obvious financial practicalities behind it.
It shows that he has no family (I guess few women would be willing to put up with him as a husband, just like Shater), so he lives in a bachelor pad, so it's a 1-bedroom house, it hardly has any decorations other than what you'd find in a magazine, meaning he doesn't spend a lot of time there, other than to crash once in a while, and there are way too many glass walls. I mean, it's nice to get a view of the ocean, but there's no privacy in a house like that other than what the bathroom would offer. (The design reminds me of the famous "Glass House," which had glass walls everywhere, save for the walls around the bathroom).
The huge glass windows are typical of LA Basin architecture, and big windows that open on a yard with high fences are very private. The house probably has more than 1 bedroom, simply because houses with multiple bedrooms are considered a better investment, and it's common for actors who have a hit series or a run of well-paid roles to invest their earnings in a nice house in a good location. Los Angeles are real estate has been a top investment for the last century or more, if he took his leading-man money from "Galaxy Quest" and maybe another show or well-paid film, then he's both doing what a lot of actors in his position would do, and he's investing his money well. He wasn't going to lose by buying a house in the Hollywood Hills!
And that's the difference between Jason and his castmates, he got paid the most back when the show was on, because he was a "star" he probably got more paying gigs than they did over the next few years, and he's able to charge more for fandom appearances and autograph shows... which means he was the only one in the cast able to invest his money in a nice house in a good area. The glimpses of everyone's homes was one of the nicer touches in the movie, it was clear that some were borderline poor, while Jason is borderline rich.
Well, let's see....the story (I'm guessing) takes place in 1999 (like the year the film was released). The dialogue says several times that the Galaxy Quest tv show ended production 18 years prior to that, meaning it ended in 1981.
Now the house design appears to resemble a style of architecture that roughly started taking off in the 1960s, and the glass thing became popular in the 80s. So it's possible he's owned the property since the 80s. Since it's a 1-bedroom house, the house and the land it sits on wouldn't cost nearly as much as some of those mansions down by the water or up on the cliffs that have 16 bathrooms and 8 guest houses. He also doesn't seem to own a car, mostly relying on taxis and limousines everyone else pays for, so that's another plus for him.
So no, I don't think Jason Nesbit inherited the house, but it's very possible he bought it years ago and still was able to pay the bills with royalties paid to him for the GQ franchise.
It's an interesting departure from Shatner's personal history (Jason Nesbit is based on Shatner, sort of), because when "Star Trek" was cancelled in 1969, he was flat broke and had to live out of his truck for a few years on the streets of Hollywood. All the money he'd earned from the show had been spent on things like parties, girls, drugs, booze, things that a stupid, egotistical, short-sighted moron like Shatner would waste his earnings on.
For anyone who might be interested, that's Case Study House 22, designed by architect Pierre Koenig, and built in 1960. It's located at 1635 Woods Drive in Los Angeles.