This talk about Selmy having "too much pride to work alongside sellswords" is absolutely baffling to me.
@Duesal is dead wrong. We quite literally see him do so for months in canon ASOIAF without any issues we'd care about.
If we want to loot this high-level martial PC, we absolutely can. We looted Liomond Lashare, who is definitely guilty of worse crimes than Barristan, so why not loot this latest moral coward who's good at swording? Is it just because he isn't as sassy as Liomond?
There's a personal component to things. Yes, it helps that Liomond is Sassy on a meta level. He's a reprobate who actually does have something of a head on his shoulders for things above swording, unlike Bronn, who was at least loosely attached to mass murder of our citizens. And Liomond was undead and working with slavers for pretty much as long as he's been alive--and we can discern well enough that while he's probably loosely grouped into the same class of people who would have treated enslaved people 'well enough', and had no proclivities toward cruelty for cruelty's sake, he wasn't on some moral crusade to free every slave he came upon. He's just a glory hound.
Bronn is a mercenary to the bone, with just a loose desire for lording power over people who did the same to him and a desire for the finer things, with tokens of wealth being the most recognizable path toward both.
So we're not above working with people who care about their own image at least a couple steps above common decency, or even baser desires.
But, unfortunately, he made the mistake of doing all of those things we don't find too many problems with (so long as it serves our purpose) by A) making his claim to fame by 'serving Kings', all three of which we as players and even as characters don't think very much of, or outright despise and B) abrogating any responsibility for the suffering Rhaella or the smallfolk Aerys burned went through by claiming he was "just doing my duty".
It's just the unfortunate bit of having personal attachment to our PoV characters own background.
Now personally, reflecting on Bronn and Liomond, and our reasons we're more open to accepting them as they are, it's because they're fun! They're roguish assholes who entertain us.
Selmy isn't like that. In an ideal arrangement, Selmy doesn't have too many personal interactions with us, in which case there's not much point to his character in the narrative. He brings nothing to the table in terms of plot, other than some vague notion of the past leading into the future, which we have plenty of.
If he does place himself as something of a character who tries to gain our confidence and attempts to interact with us, we sense that... we have no reason to really like him. We can't view him with detached amusement, like 'oh that wacky rogue, I remember I used to survive on the streets with my wits and violence alone'.
We just remember unpleasant things about the past, the taste of failure, at best, if we go with
@Azel's interpretation and assume he's just a sycophant out to improve his own image with a looser attachment on his own self importance, or with my interpretation of him as a delusional narcissist, something that wouldn't last long in Viserys' proximity anyway since he abhors self delusion in all its forms.