It would probably still be obvious that the Brotherhood was involved in his death, even if it wasn't a public display. Though, as is obvious, the arrow is just an option(though why the vanilla 40g bounty even if you aren't seen bug exists, I don't know). I've mostly used it because I hate getting the lip from the Guards. Namely when it isn't about one of them seeing me, but when an NPC cares to much. I had one instance where a companion of mine(added by a mod) reported me for feeding on a sleeping NPC. You'd think they wouldn't have cared that much.
Although, my issue with having things be a bit more, outstanding, I guess, would be that it isn't like you could kill him, and perhaps leave his corpse somewhere in Leyawiin, a bloody handprint on his chest, along with a missing finger. It could be due to the fact that this might be too outward a display, in that it would drive the Legion to hunt down the Brotherhood even more. However, it's likely that, no matter what kind of end that the man faces, it would pale in comparison to killing an Emperor.
Though nothing seems to bother me more, than characters like him. I don't know exactly what it is, but perhaps it's just that mocking righteousness that seems to exist, suggesting that mocking a cabal of murders is a good idea. Though this gets played with a bit more in the DB Chronicles mod, more than the vanilla questline.
Maybe next time I do it, no arrow. Still, I just hate the way the game handles things. Mostly, why the game has to haul me over to the castle. Can't the guard just take the bloody gold? Although in that instance, the problem is both getting seen, and if Pillida is considered a Guard by the game, doesn't matter if anyone sees it. This is mostly why I hate dealing with those two in the Next of Kin quest, although the Leyawiin guard is the worse example, if you deal with her in the Three Sisters Inn.