Mostly semantics here, but not quite on this part - accurate with the rest though.
Most stars are either predators or biofilm-feeders; there are a few that are thought to be detritivores, but I have yet to see any evidence of that assumption.
Linckia starfish are biofilm-feeding starfish; we can't replicate their natural biofilms in our aquariums, and most biofilm-feeding stars die with ~8-13 months in our tanks. Sometimes stars just "dissolve" within the first couple of weeks in our tanks for no known reason (Linckia laevigata - blue Linckias - are well known for this despite being one of the popular stars in the hobby).
Anyway, older, larger, more established tanks are generally thought to be more likely to have healthy biofilm populations in them and to be able to reproduce those populations in time for the stars to continue feeding - in practice, it's still hit and miss.
That said, the longest I have heard of these sorts of stars living even in tanks specifically designed to account for the lack of appropriate biofilm feed is just a few years (and this in tanks that are growing alternative foods for the stars, not just relying on biofilm formation in the tank itself).
At this point, the only true stars I can really recommend be kept are Aquilonastra starfish (known in the hobby as "Asterina" starfish), as they're the only ones that seem to thrive in our tanks. Other than that, I recommend brittle/serpent stars (which aren't true starfish), as they do fine.
