To start, the pistol, its a great weapon it, looks fun to use, has enough ammo to suffice (assuming upping it to 4sk), and its a precision weapon, which requires more skill to aim than an AR would at close range, which is awesome 
however the only problem i see in having it as an arena weapon start, is how much impact does it really have compared to the size of the maps, when you have map control how much map control do you really have ? ? ? when i think about this i look at simplex in halo 4, midship in halo 2, the pit in halo 3, and if you had a pistol as the competitive starting weapon on those maps, power positions which would now be considered good like, Pink 2 on midship are now considered irrelevant because the map is a little bit larger than the optimum range for the pistol to be at its most effective, but then you dont want the opposite where the range for the BR in TMCC is too far for the size of the maps, causing BR aiming and shooting to be to easy.
A video reference of what im talking about, courtesy of TSW Halo 2 vs Halo 3 vs Halo 2A [Battle Rifle Testing] - YouTube
Pistol + AR combo is currently aiding in the meta, which is run, thrust and punch, which is generally close quarters combat, at least all of these added abilities are causing this current meta (as set by the pros in the invitational at gamescom) the pistol as mentioned before doesnt provide much map coverage and also doesnt do much for stopping power for people sprinting, not even sure if this is still a thing, essentially this causes less map control (short range weapons create short range map control).<br data-reactid=".8u.1:$mid=11439211212305=298acf1d5a0814f5575.2:0.0.0.0.0.0.$end:0:$text5:0" /><br data-reactid=".8u.1:$mid=11439211212305=298acf1d5a0814f5575.2:0.0.0.0.0.0.$end:0:$text7:0" />This meta is the reasoning why the pros all prioritized the shotgun and smg over any other weapon. I didnt see the plasma caster, or carbine/stormrifle etc get picked up at all, and the bigger question is why would they ? ? ? <br data-reactid=".8u.1:$mid=11439211212305=298acf1d5a0814f5575.2:0.0.0.0.0.0.$end:0:$text9:0" /><br data-reactid=".8u.1:$mid=11439211212305=298acf1d5a0814f5575.2:0.0.0.0.0.0.$end:0:$text11:0" />Having a secondary weapon that covers both forms of combat (excluding power weapons),you would think causes more balance overall, which is great in theory (i.e. pistol for medium - close range precision, and ar fully auto for close range) but this will cause less use of the current sandbox, if both weapons cover all versatility from spawn then there is no point going out of your way to grab the ones of the map, i.e. gamescom comp. Every weapon should have a benefit for grabbing it
So if there is no advantage to dropping one of those weapons, no one will do it. Pros would only swap the precision weapons, (pistol) out for other precision weapons (BR, DMR), and close combat weapons (AR) out for other close combat weapons (smg, shotgun)<br data-reactid=".8u.1:$mid=11439211212305=298acf1d5a0814f5575.2:0.0.0.0.0.0.$end:0:$text13:0" /><br data-reactid=".8u.1:$mid=11439211230835=297e33f7cf899989a32.2:0.0.0.0.0.0.$end:0:$text1:0" />A point of interest for lore sake, pistols are inherently sidearms, kinda weird that being given the option are willing to make it a primary over the versatility of a rifle (assualt rifle although in the name is a rifle, in terms of halo it does not act as a rifle, its acts a slower shooting SMG classification, or automatic as i would like to call it), in terms of sending a soldier into a war, you would want them to go in with the most balanced versatile weapon suitable for every challenge that comes to them, not send them in with a pistol where they cant even scare a sniper into cover.
Personally you should make the primary starting weapon in arena a BR or DMR, secondary (IF ANY) should be Pistol, this gives two precision weapons to a player which will encourage them to drop one (user preference) for more versatility from weapons on the map, this encourages more map movement to weapons that would otherwise be ignored, and rewards more strategic thinking and more diverse approach to the game.
mod ploz