Regarding your poll, I would bet, if you asked if any other unit, unique or otherwise, was "unbalanced" it would not even be close to the results that this poll will garner.
If we were to take this route of balancing, where a minority with above-average but still minority support claims something is unbalanced, there would be nothing interesting left to balance in ffh. In the early versions, there were so many cries of "Nerf!" regarding the elves' ability to build in forests. You can dig up so many old threads regarding this, many considered them to be the most ridiculously powerful civ ever. Fast forward a few years and the elves still have their forest cottages, but they are no longer considered overpowered, puppets and pz's are the new scape goats. If, for every time a minority of the player base cried for a nerf, something was nerfed, this mod would be very boring indeed. And let's be clear: the poll has shown that the majority of the player base (as can be best determined by the given sample size), do NOT want Pz's to be nerfed.
Your blind spot is, you can think of great pyre zombie counters, which is fine, but they usually involve doing extra. We are not discussing whether promoted units can defeat unpromoted pyre zombies, or if certain unit combinations can defeat pyro zombies alone, to do so would be an uneven footing to start with, and would defeat the purpose of a debate on balance.
Your blind spot is time. You think that just because you researched the bronze working tech, you can immediately field a huge stack of pz's that will crush all opposition. It takes time to build cities, time to improve land, time to build infrastructure, time to build an army. Building a stack of 12 PZ's, assuming a beeline to BW, could easily take 30 or 40 turns
after getting bronze working. And then you have to worry about a counterattack, a backstabbing neighbor, etc. Upgrading warriors won't help too much either because someone has to stay and defend your own cities. And then it takes time to get from point A to point B. And let's not forget, you have to build a city to hook up copper, else archer defensive strength will be able to create quite a problem for you. And anything less than 10-12 Bronze promoted PZ's has no chance at all against a heavily fortified opponent fielding archers or whatnot.
And ALL of the above assumes a beeline to BW on the part of the Sheaim, which is generally horribly inefficient in the long term unless you start with
gold/gems/large quantities of wine in reasonable distance of your starting location. Even then, you'll still want for cottages and lumbermills.
So your saying in all that time, a competent opponent will not be able to muster a defense capable of repelling 10-12 Pz's? And keep in mind, the Sheaim have no expansive trait, no particular warrior rush capability. Other civs do and will likely have larger empires with more cities, more production, more research, more resources, and already larger armies by the time you
start to produce PZ's, which means you'll need a larger defensive army. Yay, more delays. You're already playing catchup, against a competent opponent. And all of the above assumes
you don't get attacked by a belligerent neighbor like faeryl or tasunke, who can be quite annoying.
To say nothing of MP, where all of your neighbors that
play to win may well ally against you to stop you from amassing your pyre zombie nuisance army in the first place, so that they don't have to bother with countering them in the first place. And if you are in a situation where you can't be attacked, the reverse is (probably) true and you're probably too isolated to rush a horde of PZ's before they can amass counters.