Washington DC is nowhere near being the most expensive place to stay.
Tons of hotel rooms between $150 and $200/night when there's no holiday going on. I live in a little town and the hotels that aren't complete dumps start at $120. Flights from LA to DC start at $150 or so, which isn't any more expensive than flying to Houston. A rental car in DC can be had for around $100/day which is about the same as a rental car in Houston.
As for accessibility, booking one flight and one hotel stay to see all the exhibits in one place is far more accessible than booking multiple flights and hotel stays to visit exhibits scattered across the country.
Finally, I would really like to see the source that backs up your claim that "only a fraction of American students and veterans have ever seen the Space Shuttle on display, or the original Smithsonian museum itself". I'm fairly sure the source is you just making shit up and presenting it as truth.