It's a neat piece of design space that allows certain character types to be more desirable without having to boost them in other ways.
Maybe but my understanding of the core, special, rare is that they represent how common the type of soldiers are in the army in question. Like if I was able to take greatswords as a core choice I certainly would and produce an army which had 2 large units of greatswords and therefore I would have an empire army that had no core units in it. This does not seem to me to accurately represent what an empire army is.
It might be better to shift some units from special to rare and then let you have them in special if you took a certain character. Its not what GW have done though.
7th ed Warrior Priests allowed one unit of Flagellants in Core. I can't remember anybody whining about it. It was esteemed as very good design by GW. Fluffy, and not OP.
Greatswords should be a 0-1 per 2000pts choice, and then allow the Elector Count to take them in core. Because that would be exactly as it should. Maybe an Empire General would need to buy a small upgrade to make him an Elector Count, which would then open some choices. I'm seeing several minimum units of Greatswords played as Stubborn chaff, and that's just so totally against the setting.
Talking of a wishlist, I just played against Brets who have the Battle Pilgrims - Stubborn, Heavy Infantry, LA+Sh. Always include the Grail Reliquae and a Grail Vow character nearby, and the unit is Unbreakable. For 8pts per model, and you always want the Grail Reliquae for 65pts (6 Wounds, 6 Attacks to the front, solid psychology). It's a great tarpit unit, everything is geared towards that role.
Flagellants should definitely have something similar. It's Empire, so it should be bigger: 50x100mm base war altar or some sort of penitent machine should fit the bill. Also great opportunity for centrepiece modeling without bringing another lone monster or STank.
In general, a religious nuts army list would be fun. Make infantry strong with a blanket special rule (immune to fear?), at the cost of bringing no special knights or knight commanders. Possibly Flagellants in special and artillery in rare. Plus some sort of new unit in special (because after removing cav and arty, it would be too empty).
-Zyg