Yes, because how dare someone want the person responsible for many terrible things to be brought to justice or stopped from causing even more damage.
If you want someone to respond genuinely to this, then I'm game. If this post ends up being over a thousand words long, dare I say you did bring it on yourself for requesting a serious discussion. I'm a very boring person, I know. (p.s. I'm not a philosophy student, and I'm not an expert in ethics. If you are, I'm really really sorry).
Firstly, I'm going to question your use of "many". So far, we only know that Solas directly caused one bad thing - giving Corypheus the orb. Indirectly, many bad things have been caused by Corypheus since he gained the orbs power - he opened the breach, killed many members of the chantry, the templar order, and the former circles, introduced red lyrium usage into the templar order, managed to enslave half of the mages under the arms of a Tevinter supremacist cult, and encouraged fighting between templar-mage factions which left many destitute and penniless. I could go on and on - but that's half the events of Inquisiton. Either, indirectly, 'many bad things' is an adequate description. Since the breach, Corypheus has been the cause of lots of war, death, and poverty - serious bad things.
We come to our first dilemma. Do we hold Solas responsible for his direct actions - giving the Corypheus the orb - or do we hold him responsible for both his direct and his indirect actions?
Solas' direct action was mostly harmless when isolated from what it caused in turn - he gave Corypheus an object of great power. I think this approach to ethics can be very limited. For one, Corypheus is someone of dubious moral character. For two, the orb is an object that can cause devastating consequences, and any intelligent person (which Solas claims to be) needs to either a) trust the recipient not to cause those consequences, or
control the recipient's use of the object somehow. Only blaming Solas for his direct action is equitable to giving a small child a loaded gun, and saying it is the child's or the gun's fault for their death. Because the orb has a great amount of power - it's not like giving Corypheus a bauble - and because Corypheus is not particularly trustworthy (although we don't know what access to information about Corypheus Solas had when he gave him the orb, but we safely can assume he is not trustworthy) - we should therefore assign some level of blame on Solas for that direct action (even in ignorance of the indirect action that he caused).
However, unlike a parent giving a small child a loaded gun - where the parent is quite knowledgable of the parameters, they know what a gun is, they know how it works, they know their child has a limited knowledge of guns, they know their child is curious, and thus they've figured out, without thinking too hard, that it's a horrendously stupid risk - we cannot assume the same of Solas. We blame the parent for the child's death because of that knowledge; can we fairly do the same for Solas?
If we are judging based solely on direct action - then I think we can correctly accuse Solas of being incredibly stupid. But given the limited knowledge he had about Corypheus, and (I assume) some plan of controlling and directing his actions, not necessarily malicious. I think giving a child a loaded gun can be potentially interpreted as a malicious action - there's one obvious bad consequence of that, someone innocent gets shot, therefore, unless you're ignorant of the parameters, or want an innocent to get shot (which is a malicious action), you don't give a child a gun.
Why am I making a point of looking at Solas' intentions? Surely the most important things are consequences? (That's a matter of fierce debate, but yes, for the moment, I'll happily concede consequences are more important, because I agree, although I think in general when people have good intentions those lead to better actions). Because we're talking about responsibility. Justice. Is Solas as responsible for Corypheus' actions? About as responsible as Hawke was for letting him out, not knowing that Corypheus was immortal and could take over wardens' bodies, probably. Lack of malicious intent, and likely ignorance, rules out the possibility that we should judge Solas for the entirety of the events of Inquisition as if they were his direct actions.
You could argue: should a god know better? We could get into a debate about what godhood and divinity is there quite quickly (since that varies massively even in existing religions), so I might just say for the moment that he's just a very old, powerful mage. When 'normal' people are able to bend the rules of physics via magic, the distinction between magic and miracle becomes much harder to discern anyway.
So - I think, given the risk involved in the direct action, Solas should be held partially - partially - responsible for his indirect actions, although Corypheus' actions should not be treated as if they were his own.
You could probably argue now that given that he's got a partial responsibility for what happened, why should you cut off his head? At which point, I'd concede the argument, and just ask you exactly how useful would that be? If you seek justice, you already got to wipe Corypheus from existence. Is that not enough?
As for the latter half of your claim 'stopped from causing more damage', we don't know what Solas' plans are or what he intends to change. We know that he's wholly committed to his cause, and that cause involves helping 'the people'. We don't know anything beyond that. It may not even be harmful. Anything else is really just conjecture. I think to kill him for 'potentially being dangerous' without much evidence at all is a pretty nasty precedent to set as a lawmaker. I mean, if you Inquisitor is an ass, or suspicious, fair play, but hardly the moral highground.