For the simple reason that no one actually knows if killing all the Old Gods would solve anything. It could have the opposite effect and make the situation worse.
Darkspawn toil in the Deep Roads, digging and searching Old Gods to awaken and turn into Archdemons. They are drawn by the singing. What happens when there is no singing ? We know what happens, Darkspawn go mad. That was what happened to The Mother in awakening. They would storm the surface and slaughter everything and kidnap women to breed with since there is no music to guide them to a singular purpose. Before one points out that you can kill off Darkspawn, they always come back. They are numerous in number and for practical purposes one can even assume them to be infinite.
In fact, I would posit the idea that the notion that once we kill off all the Old Gods, there would be utopia to be a bullshite myth. It is a lot more complicated than that. Which is why I also think sparing the Architect is a good idea since if you want to kill off the Old Gods, you need an alternative life path for Darkspawn since they do not do anything but seek the Old Gods. Making them sentient might create a situation where one can actually kill off Old Gods without possible ramifications. Yes, his plans are barbaric but he has been refining his goals over time.
Fundamentally however, Solas is the type of character who does not believe in doing something without purpose. He hates YOLO and actions done via lack of thinking. Grey Wardens to him do this as they try to just kill off the Old Gods without trying to understand them or trying to understand the ramifications of just killing Old Gods who are not Archdemons.