It makes sense a quasar could blow out the gas and dust away from the galaxy, cleaning house and eliminating the raw materials necessary for the creation of new stars. However, there are still old stars there and if the quasar phase lasts a shorter time than the lifetime of supermassive stars – a few million years, then there will be those large stars that go supernova, and smaller stars that ejected planetary nebulae and solar wind particles from most all stars that will reseed the galaxy with star froming material.

It's then probable that the material will gravitationally clump and be pushed this way and that by additional supernovae and reestablish star formation, at least in the disk of the spiral galaxy.

Note that the milky way – our galaxy has about a 3.7million solar mass BH. It has globular clusters in the halo that appear to be about 10 billion years old and should have had this AGN quasar period. Yet, we see the sun as about 5 billion years old and we see plenty of galactic smog (gas and dust) and we obviously see ongoing star formation, from some in the first phases to the existance of very high massive stars that have lifetimes far shorter than the time since the dinosaurs went extinct.

All of this local evidence refutes the basic notions of the article unless one adds the notion that the stars are reseeding the galaxay and forcing the return of star formation. You'll note the sun is not a first generation star nor probably even a second or third generation one. The material the sun formed from was ejected by earlier stars.

Since ellipticals evidently contain similar sized supermassive BHs and have no modern star formation (and no significan amount of interstellar dust and gas (and the same goes for globular clusters), it is possible that AGN and quasars could have gone on inside there too and that perhaps there were not sufficient numbers of very massive stars present to reseed – or perhaps the density of stars was so high in these that forming conditions could no longer exist after the first stars were created – or perhaps that the AGN / quasar phase happened shortly after the very massive stars went supernova.

That's an oversimplification. The dwarf Seyfert NGC 4395 has a BH, but no bulge, and other likely examples are known. Maybe they mean that central BHs don't get "supermassive" unless you have a large classical bulge.