Maybe im wrong with math or i forgot something than,
but a fighter of lv 11 (where is probably where it should shine more due the 3 attack per round) with a GW and GWM feat, deal something like 21 (3d12) + 30 (GWM) + 15 (str) = 66 (plus eventually superiority dices and action surge, plus around a +2/3 due GWF style. I suppose we can consider around 80/85 the real total, bcs of the limited use of SD and AS)
Paladin 11 lv Oath of vengance: 14 (2d12), +10 (2d8 Improved smite) + 20 (GWM) + 10 (str) +7 (2d6 assuming he cast the spell) + 27 (+1d12 + 1d8 +10 +5) + 3 (GWF) if he is in haste (and he shuld be lol) with advantage for one minute if he need its = 91 plus he can smite with a max of 3rd lv slot, so he can add 11d8 more (at least 1 slot of 3rd lv is used for haste), for a total of 146 without crit (but having only 10 spell slots and only 3 of 3rd level, the real dpr should be around 100, but honestly, this is neither his stronger aspect, bcs this guy with all that auras, heal power and heavy armors, is made for be the real tank in my opinion, plus deal a very huge ammount of damage, He can ebven go board and shield and still deal tons of damage with a demigod AC and d10 for hit points, maybe it is a bit overpowered compared with other martial classes, considering he is also half caster). Multiclassing sorcerer give lots of advantages that ill not write here, but he can even quicken "hold person" with sorcery points, and auto crit with smite on it in the same turn...something really brutal.
my HW with shapeshooter, if he get the 3rd attack on a 3rd creature, at lv 11 deal 10 (2d8 planar warrior) + 30 (Shapeshooter) + 15 (3d8 bow) + 15 (dex) + 5 (1d8 hunter's mark if i can cast it on the first round)= 75 (but its below this bcs i often have to choose between moving the mark and deal the 2d8 force damage, as both are BA)
a pure arcane trickster at lv 11 use SB just 2 minute for long rest, he deal 10 (2d8 SB) + 18 (5d6 SA) + 25 (5d8 BB) + 5 (DEX) = 58, and if he go for a second attack via BS 6 he lose significantly SA, being anyway better than the pure AT.
A Barbarian is kinda similar with the rogue output, while probably the zealot one is few under the 70 dpr.
i never played a monk so i dont know so well its mechanics, but many people said me he keep being a bit underpowered.
Bards, Clerics, Druids are for sure below as melee output
warlock i suppose its below but honestly, maybe i miss something about it, as i played it pact of blade but multicassed with a barb bear totem (just 3 lv dip barb for abuse armor of agathys, get advantage at will and some melee damage output with rage) keeping AC intentionally low to 17 for be hitted kinda often. For what i needed it works really well, but i just need to cast armor of agathys and fire shield, maybe some darknes sometime that being a drow i casted from racial. As a pure warlock i more often see the version that spam eldricht blast and that i find so boring to play. Anyway also my barblock i think it deal around 70 per round at 11 lv considering everything also out of turn.
our guy with a SB of 3rd lv (but he can upcast to 5th lv if he want) and BB applying (and i found out that also Jeremy Crawford in practice allowed to do it, bcs seem this specification was born for other intent than nerf SB, i just dont get why there is still no errata, probably bcs "it counts as a simple malee weapon" it already refers to everything, including price and so including how many gp is worth, but you can find more details here:
) deal anyway something like: 15 (3d8 SB) + 40 (8d8 SB + BB) +10 (dex assuming he maximize it) = 65 (and even if we want to read it strictly RAW he can use Spirit Shroud and a normal rapier with BB for a very similar output damage), and with contingency i suppose will be kinda easy to upcast it to lv 5 slot for still more damage, but if we dont have SB the output go down to a low 45 that is pretty awful. If i didnt miss anything (which is anyway possible and near to sure

) the damage output in malee for BS is anyway kinda hight if use a shadow blade (or spirit shroud) even without spend an hight lv spell slot with SB (3rd lv spell slot is already ok).
Anyway what i mean is, im not sure its so true that BS is not good in deal melee damage, for sure there are stronger dpr (as stronger tanks, any heavy armored class with shield proficiency and 3 lv dip in barb bear totem tank better due the huge ammount of hp and resistence that can ignore crits), there are some class and for sure some multiclass build better for it, but he is also (or well, basically) a full wizard and when cast anything instead than SB is more usefull he can still concentrate on that specific spell and attack melee with just a rapier and BB, but when there is nothing better to cast, or when he want to save spell slots, i more see him good for deal melee damage with SB than just stay there to get the more attacks he can with blur (except against some enemy hitting really hard, but many of those enemies often have "blindsight"), especially in my party that count on a paladin, a cleric, a moon druid and a rogue, except the rogue, anyone else tank kinda well and together they get most of the attacks.
Honestly, im starting to think that i want make him sort of antimage character (also for background's thematic reasons), having so many big guys in the party helps i suppose, and maybe pick and upcast false life (even to lv 4 later on, but lv 2 in the beginning) can be a good idea also for avoid to go down by crits that before or later gonna hit as blur, blindness or even greater invisibility, dont work with things with blindsight.
I can even think to pick mage slayer as feat, making this progression:
+2 dex, +2 int, mage slayer, + 2 int, + 2 dex or changing one stat increase with war caster or resilient if i need to boost concentration.
i'd like to get the feat also for thematic reason, but also bcs it help with saving throw if i get near the caster, bcs normally a fight dont have more than one offesìnsive caster and at same time can (very few times honestly) boost dpr with OA or easier broke the enemy concentration on some nasty spell. The problem keep being the odd con, but if i want int and dex both maximized seem it must stay odd except get resilient.