A local house of rulers which persisted no less than half a millennium and governed the country's most densely populated zones can't be deemed irrelevant or obscure in the framework of that country's history.
The Ilkhanids were actually yet another Shia Muslim dynasty of Iran (although of Mongol origin, since they were the inheritors of the Mongol invaders), which like the Buyids lasted for about a century. And, they did rule over most parts of Greater Iran.
In fact, the Dome of Soltaniyeh near Zanjan, built on orders of the Ikhanid shah Uljaito Khan, was originally intended to host Imam Ali (as), ie the first Imam of Shia Islam. However Uljaito failed to accomplish the transfer from Najaf, and so in the end the Dome became his own resting place.
Here is a more comprehensive list of Shia dynasties of Iran prior to the Safavids:
As this list shows, the Buyids did not represent an isolated phenomenon. Although many of the above were local rulers or only controlled parts of Iran, truth is that between the Arab invasion and the Safavids, it was not rare for several Iranian states to coexist as neighbors, whether they were governed by Sunni or Shia kings.
During that period (7th to 16th centuries AD), the majority of royal dynasties in Iran were of Sunni Islamic denomination. But, to say that there were no Shia Islamic rulers, or that these merely constitute some isolated and historically insignificant occurrence would be wrong.
This is a map of the Buyid empire:
They did rule over the great majority of population centers of the western half of Iran. The Justanids, by the way, which governed parts of the neighboring Sallarid kingdom, were Shia Muslims as well.
At any rate, the notion that the Safavids isolated Iran culturally due to making Shia Islam the state religion is not accurate. Both the Ottomans and the Mughals continued to use Persian as a lingua franca way beyond the Safavid period, and Iranian culture continued to shine beyond Iran's borders.
The thing is that the great Islamic caliphates had come to an end, or regressed in their geographical expanse. Another issue is the arrival of western colonial powers from the late Middle Ages / early Renaissance, and especially from the 18th century. It is these factors which at times led to a relative reduction of exchanges between different parts of the Muslim world.
Historiographically speaking, Ali Ibn Musa Reza's (as) emigration to Iran does not stand to debate. Nor does the fact that Mashhad became a center for pilgrimage with special significance for Shia Muslims right from the 9th century.
This is all part of Iran's pre-Safavid, Shia Islamic history and heritage.
