This thought came up in a recent game, where I was running Intolerant for the first time ever. Why not allow for inquisitions to purge holy cities? This could work very well with the holy city relocation mechanic. A good real life example of this would be Zoroastrianism. Pir-e Sabs, Pir-e Seti, and Pir-e Naraki are the preeminent pilgrimage sites for modern Zoroastrians. Pir-e Sabs is used for the Holy City Shrine, and the other two are Zoroastrian's state religion wonders. All three share a similar tale. They are where prominent Zoroastrians fled from the Muslims, and were subsequently martyred.
In game mechanics, whatever the real city of Zoroastrian's founding is would have been inquisited by the Intolerant running Arabs. The holy city would then transfer to another suitable location, and the Zoroastrian civ in question begins building the Pirs, all of which provide defensive and/or military bonuses in order to begin the long fight to reclaim their homeland.
Most of the religions we have in game are completely dead in the modern day, in many cases because people of a rival faith destroyed all the remaining vestiges of their religious institutions. It is slightly odd we can not do the same.
My suggestion is to allow inquisitions to be performed on holy cities, but it will have a very small chance of success, and will automatically relocate to another suitable city when you do. Currently the only option for eliminating rival holy cities is to destroy the city they're in, which isn't always a realistic option, especially if they're your cities.
Another thing I noticed is that the AI, for whatever reason, simply will not perform inquisitions in their cities. In this particular game I was playing, I converted the entire continent to Islam, then gave everyone on the continent I could the Fundamentalism technology, and paid them well to adopt Intolerant. After a few turns I could tell they would need some further help to purge other religions, so I started gifting inquisitors to my allies. I built three per turn for at least 10 turns, each time giving away my inquisitors in the hopes the AI would purge the other religions. This did not happen. The AI simply moved the inquisitors to their cities and let them sit there.
Lastly, why such a low limit on inquisitors? You can only build three at a time. This makes Intolerant a very lackluster civic to run. This number should be raised to 10, or perhaps 15. You can try running Intolerant temporarily and switch back to some other religious civic, but this doesn't work very well. The minute I switched to State Church in my game, 10 of my cities were immediately converted to Hellenism. This seemed like a strangely rapid rate of conversion, considering the AI had not employed missionaries in this.