Bhelen wasn't walking around the streets of Orzammar butchering people... until then. Harrowmont had only known him to orchestrate the killing of one brother and framing of his other brother- something others could've done (did do) for him, something done some time ago behind the scenes in the Deep Roads, and something done when no eyes were on him. It is fairly established that civil war could happen any moment, however, so bodyguards were in order.
As it happens, watching it again, it seems I was mistaken: Harrowmont does have bodyguards- or what appear to be such. The one is killed with a single blow by Bhelen's loudest thug (someone we never see again), but the way he speaks is not like a Harrowmont guard. He calls, "Handlers! Separate these deshyrs (meaning both Harrowmont and Bhelen entourage members)! I will not have Bhelen inciting a riot!" He doesn't appear to single out Bhelen due to support for Harrowmont so much as due to Bhelen's greater aggressiveness. The shiny-armored guard stands next to Harrowmont in the scene, but if he's not a Harrowmont "handler," who is? Whatever the case, and whatever the violence in Orzammar, street brawls and riots seem to be starting just then, not something normal in Orzammar.
But you're wrong that the other guards run off, leaving Harrowmont alone before he can even get up. The one bodyguard initially standing to the side and behind where the shiny guard was holds his ground entirely, looking like he's sizing up whether he'll need to do battle, clearly surprised at the resort to brawl standards among deshyrs in the streets, but the other not only holds his ground, but also helps Harrowmont to his feet. Then all three simultaneously take off together. I'm not knocking your impression, but I'm getting a different one seeing that scene.
Another part of the scene was the large number of bystanders, most of which having the deshyr staves, so there were also plenty of witnesses- witnesses from the nobility and likely Assembly- another reason to not suspect Bhelen and his "seconds" of readiness at that moment to immediately resort to violence in the street. Surprise, surprise- Bhelen's a brute.
Yes, Orzammar's society is brutal systemically. This is an endemic problem for the dwarves- in fact, the chief reason for their decline, the inability to remain united against darkspawn and the constancy of loss to violence. I'm not sure how this somehow warrants backing the most aggressive thug, however. In small street gangs, there is generally nothing but brutality that establishes predominance- or in any case simple brutality is sufficient. (Not efficient, but sufficient.) In the governance of cities that brutality only breaks down the ability of the society to function on a large scale, as Bhelen's brutality already has the city at a standstill when we arrive. So I suppose it depends then on how one views Orzammar- as just another gangland turfwar territory where you essentially may as well endorse whichever thug is going to prevail, or as an ancient civilization with laws, culture, taverns, education, and the sophistication of advanced social organization which requires a more capable leadership that can appreciate and attend to such concerns and institutions. I tend to favor promoting leadership of the latter sort regarding Orzammar- despite how commonplace thuggery can be, at least if my characters are looking out for Orzammar's best interests. Orzammar may be suffering from rampant fratricide, but it doesn't stand as a gigantic bastion of it. Cities only stand despite it. There are Dagnas and Baizyls and Garins and Deneks and all sorts of non-thug citizens who are living decent lives quite apart from the violence and demonstrating the neglected side of what remains of dwarven civilization in DAO... And it's they who I choose a leader for... albeit between two ultimately insufficient candidates.
I also don't see the opposite of lamebrained thuggery as simple compromise. Bhelen was out for the jugular. There was no compromise to be had with him. But beating him doesn't require more lamebrained thuggery. There are more tools available than that. Alas, Harrowmont doesn't have the leadership stature to win the required majority of the Assembly by persuasion and example... and I attribute this partly to his having been only an advisor his whole life, but also to the weakness of the forces he was seeking to rally- i.e., regressive nobles reticent to needed change. Bribery is just as traditional in Orzammar as oppressing the casteless. And ruthlessness against the latter is something Harrowmont excels at if you give him the Anvil. If you're going to say that the whole system is corrupt and both candidates are immersed in it, there's no point saying Harrowmont isn't ruthless enough... It's just that Bhelen's ruthlessness involves willingness to eliminate his entire family and former advisors- and anyone else seeming to be in the way- so he can take the throne. Harrowmont's ruthlessness involves willingness to eliminate the entirety of the occupants of Dust Town to further the cause of one portion of the Assembly.
Still, I can imagine a different Assembly member rising to that occasion to call for reforms similar to Bhelen's and yet who also knows how to rally people to that cause and orchestrate them against Bhelen, winning away Bhelen's supporters among the Assembly as well as some of Harrowmont's, possibly even avoiding a violent confrontation- other than perhaps with Bhelen and Vartag themselves at some point- particularly given the imperative of meeting the darkspawn threat. My returned DN would certainly have relished the opportunity... if the writers hadn't written him out of the running arbitrarily...