Each vaulted part, warframe is "fomo". They unvault sometimes for a limited time, again, fomo. You can pay to get a better chance by buying platinum and buying relics off the market.
They wouldn't have to vault anything, every prime warframe could be available (maybe except excalibur since that was for early adopters, and umbra was the "prime" version everyone got).
No, each vaulted Prime rotates in and out of the vault on a well known and predictable timetable. Ditto the Duviri Circuit rotation, except that there its a much shorter rotation.
Outside of some completely optional fashion choices the difference between prime and non-prime is completely irrelevant.
The stat buffs a prime gets are irrelevant now with the archon shard system.
Biggest thing is that some of the primes are easier to get(e.g.Equinox, Nezha, Grendel) but again, the duviri circuit makes that point moot.