I'll do the obligatory: "Then which ones would work?" A lot of these are interesting outside of 6v6.
Slightly less self-damage for the Detonator wouldn't be that bad. Double clip doesn't feel necessary, but more horizontal self-pushback might be the way to go. Gives the pyro more mobility for mids, maybe. You may also gotta tweak the other secondaries, then. Btw, the detonator/scorch shot can destroy stickies.
How about upon airblast, timer explosives (if almost primed) reset to half their arm/explode time? Pyros can't fully shutdown demos, but they can increase their support role. With the reduced airblast cone (I think it's currently a box, but I may be wrong), it would take slightly more precision. I don't think you should speed up the airblasting rate at all; it's relatively fine in normal pubs.
Mini-crit projectiles should stay, but reflection jumping should become more viable. 40% damage reduction [ignoring mini-crits] for reflecting projectile on self.
The pyro shouldn't change sticky teams; would make pyros a bit powerful when teamed up with a sentry. Minorly, sticky-pushing adds slightly more game dynamics as almost every other projectile changes teams.
Pyro flames should obviously be more accurate. Particles further away already last longer, and more damage at range may encourage players (in certian situationas) to touch faces. That last part is something that Valve wouldn't want in this type of game. And pyros are already powerful against new players (Valve also has an interest in not forgetting about new player retention).
That entire Eureka Effect thing wouldn't affect 6v6 in any significant way. By the time you get to use a sneaky play, they'd know to expect you.
In terms of pubs, that would definitely get used. Sacrifice personal survivability with flanking and "mobility" (mobility is basically extra health; see Scout). I do feel the team-oriented dispenser/teleporters should get slightly buffed (you're losing a level 3 sentry), like 20% faster dispensing/teleporting.
I doubt the Heavy can be made a constant mid player, mostly due to his inherent purpose of tanking damage and 400+ health slowing the normally quick mid-game. He's used relatively often as a last point off-class (read: lots of health). Off 6v6, people wouldn't use the GRU if it had any passive health disadvantage. If there was an item that could be used where the heavy can't get overhealed (maybe that would work?), it'd have to work for pubs [and eventually, 9v9/highlander/whateverValvewantsittobe].
I think a Lunchbox slot would be the thing that makes everybody happy. Doesn't make the heavy extremely powerful while giving him more options than his currently generic self. As a side-note, Heavy shotgun's alt-fire could toss a recharging medium ammopack.
Sniper is the class that, if removed, would have the least impact on pubs. Give so much more freedom in highlander. Make scout/sniper mains on 6v6 sad. But it's a unique mechanic compared to other classes.
Snipers should feel useful to inexperienced players, but a 450 damage easy-bodyshot without risking yourself is way too much. I feel sorry for that medic on higher-level games. Now, fully-charged bodyshots will probably still do a ton of damage, but 450 at all ranges away from risk is excessive.
At close enough range, headshots do mini-crits: 68+ damage. Still rewards skill at close range, while insuring godlike snipers can't OHK at a range they should always suffer at.
I like the idea of keeping the spy disguise on backstab, along with doing some good damage. However, I feel more positive/negative stats should be added so it's more useful in pubs and less annoying on highlander, also. Ideas can include decreased overheal, regeneration time, etc. For the DDS, the thing can be entirely reworked to where you're a little vulnerable in the front, but very resistant to back-damage; an aggressive, retreating weapon. imagines snipers battles where snipers keep doing 180s
I think the only change that affected really 6v6 was making the pyro more useful. The rest could be good for pubs/highlander/somethingelse.