That's missing the point of Inquisition.
Long story short, it was created not as an instrument of self-criticism, but to crush heresy (and Judaism, that was understood as such since the 1210's) as being seen as a social threat (basically, in a society that base itself on one religion, and where both royal and pontifical power grow, understanding themselves trough roman law, non-christian bodies were seen as an annoyance if not a threat to society and authority).
You had inquisitorial inquiries and even trials on disciplinar matters IOTL, but the Inquisition as an institution was created against Heresy (including Non-Christianism as a whole)
You could make Inquisition nicer than regular justice (and admittedly, in the great lines, it was, would it be because they actually go trough a trial process and limited use of harsh punishments and torture) but making it somewhere else than an institution devoted to this would at best require several PoDs since the Xth, that could as well butterfly away Moriscos.
And this is as far as it extents, firing people from their jobs.
That was actually somewhat the case with
inhabilitas. Its usual consequences were being ruined and living in misery.
This instead of burning people at the stake or torturing people.
Actually, Inquisition didn't killed anyone itself : technically the secular punishments were gave by the temporal authority. Of course both juridictions co-operated but it means that Inquisitorial trials were relying on, say royal authority to function and had eventually less and less room for purely religious punishments.
It's to be noted that the actual inquisitorial trials resulting on death on a stake are limited (I merge there the "condamned is killed before being burned", the "condamned is asphyxied before burning" and the more rare "actually burnt"). Maybe 1% of the trials end as death condamnation, 4/6% in some specific periods (considering you had several mass executions in these periods)
While being killed for religious matters is clearly not the definition of "nice", it's to be compared to temporal matters on it that were far more expeditive (for exemple, the number of witches executed in Germany represent roughly 423% of the number of witches executed in Spain)
The problem isn't the killing part, or having the Church not being nice, it's the social (heck, even structural) refusal of late medieval Castille (and globally Europe) to deal with religious communauties other than itself, and the refusal of Moriscos to either acknowledge Christian takeover.
From that you have all a building of mutual hatred that ended badly for Moriscos as they had the lower end from the start : arguably, two societies that want to have nothing to do with each other, violently reject the very idea to accept it wasn't going to end well. You can still see this today, unfortunatly.
If we're to deal with Spain only, breaking Moriscos as an organized and unified communauty is the only way I can see to allow a more important Arabic legacy in Spain. (that is quite important IOTL)