- Druids are versatile and can be good in melee. Flame blade is a good weapon. The broken concentration is the problem, not the weapon.
- "Probably" is not an argument but anyway, you can wildshape during combats.
- The bear and the bird are usefull in combats and the bonus action add a lot of versatility. The wolf is also interresting in a group (critical hit).
Your image mirror can avoid 3 attacks. Such is the bear depending the ennemy, without spellslots, 2 times/long rest. Its damages are good for the first half of the EA. It become a meatbag after that, which is fine to me because you have all your spellslots to deal damages.
It will probably be upgraded at level 5. I think a multi attack will become necessary.
Battlemasters are playing with greatweapons because GWM is broken because of the so easy advantages.
I just ended a solo playthrough with a moondruid.
Anyway looks like you want to argue. I don't and I'm tired.
Good night and good luck with your suggestion

They cannot be good in melee if the weapon they can use, which is 1h clubs and staves unless you are an elf race, does not scale well with Shillelagh because while the rest of the classes can use +1 enchantment weapons and rares, your Shillelagh compatible clubs cannot. Moreover, flame blade cannot be coated with consumables, which is like 50%+ extra damage currently in EA, so this fall off only gets worse.
- They are not useful in combat. You are literally wasting an entire turn turning yourself into a target dummy and prolonging the lifespan on your enemies so they can pepper your team with more crap. Misty Step is a streamlined raven. The only remotely useful form you mention is the Wolf, if it manages to live more than a single turn considering the damage Bulette, Githyanki, Redcaps, Ethel, Specter, or even the Gnolls or Goblin temple fight puts out.
- Avoiding 3 attacks with 30 AC is more damage mitigated than bear form will ever mitigate, and then I'm left with a 19-21 AC humanoid form to boot, that can keep doing actually meaningful damage and heal my teammates on top. It's not even comparable. It is not fine to transform animal forms into basically useless meatbags. They just become more inconvenient to use arcane wards and completely waste your specialization and class mechanic. Stalling is a suboptimal strategy, I don't know how else this can be spelled out for you. You mitigate far more damage bursting down threats than you do trying to tank them.
- Battlemasters are not broken with GWM; I am legit always speccing Lazael NOT into GWM, and she's still the most reliable CC application member in the team due to CC spells sucking ass in accuracy even from high ground while Frightening Strike from backstab has a minimum landing chance with Bless of at least 80%, and it does 14-24 damage noncrit to boot. Does Halt do that with its pitiful 60% hit chance? Of course not, and it costs a far more precious spell slot while not even doing damage. Then there's the fact I can slap a wyvern poison, or any basic poison for that matter, dip the weapon into fire, and get with action surge 2 hits for well over 60 damage total on 105 HP lv5 bosses far more reliably than any spell can besides Magic Missiles, which even at lv2 with the necklace does less damage than a Lazael burst. Won't even mention rogues, because sneak attack is dumb.
The other classes just are WEAK as are their mechanics.
I'm glad you finished a playthrough on a moon druid. I also finished one as a Kelemvor Light Cleric, a far inferior class as clerics are crippled in design even worse than druids. But completing the EA is not proof that a class's kit is well designed and properly balanced to the others.
But on issue (2), don't we still benefit from the magical qualities of the club/staff when using Shillelagh? For example, if we are using a +1 staff, wouldn't it still be 1d8+1+wis modifier? I thought the spell just changed the weapon die to d8, and let you use your wisdom modifier instead of strength for attacks and damage. So as long as we get magic clubs and staves, I don't see why any change to the spell would make sense. Our clubs and staves could still be magic on their own, Shillelagh is focused on the damage die and the ability score we depend on to attack and damage.
And that kinda follows with (3), where Shillelagh should not be what makes us decide between which weapon to use, the magic qualities of each would determine that. Got a nice club + shield, use that. If you got a magic staff that lets you cast a spell you like, you use that, the cantrip is just an extra, but the weapon qualities themselves would determine which we decide to use. I'd be generally skeptical about letting a cantrip increase magical attacks/save DCs, those should be qualities reserved for the weapons themselves. I don't want a cantrip to invalidate magic items we receive.
I do however, think that staves need to be versatile weapons, per PHB, so that druids can still use them with their shield. Then Shillelagh would be used to increase the one handed d6 back up to a d8.
Edit:
On animal forms, while I do disagree with your changes, I also think the problem you are trying to resolve is valid, as a result of Larian nerfing the combat ability of the animals that we can shapeshift into. The wolf and bear forms should already have multiattack, and so the damage they deal is subpar. While I do think some of the changes you advocate for would be negative (ie, you should have a lower AC while you get free extra hp in a form), I think the forms should be returned to their TT power level.
The problem is there's not a single club usable by a non-elf druid that is +1 enchantment in EA, and staves are bad.
My other problem with your suggestion of making staves versatile is that it only exacerbates the problem of making shields mandatory for anyone but great weapon or DW martial classes, and quite frankly holding a two handed staff with a shield just looks so dumb. It's not the iconic look of a caster. Which is why the benefits of a staff should go toward being a desirable weapon for classes that want to cast. There should be viable, competitive alternatives to using a shield. I certainly don't enjoy kitting all my casters in medium armor proficiency with shields because 19-21 AC over 14-15 AC with mage armor and a staff that provides no benefit is too good to pass up. The only time you consider otherwise is going Warlock initiate on Wizard to try to get slightly more damage with Ray of Fire+Hex than Magic Missiles Rank 2, but at the cost of being far more unreliable in accuracy (imo not worth trading off 4+ AC).
Granted, the latter argument is more of a commentary on how awfully implemented casters are in this game, and how the Concentration mechanic on top of the limited spell slots is crippling their gameplay. Someone has to be on mushrooms to believe that spamming Eldritch Blast as a warlock because you got 2 spell slots and one is reserved for Hex happens to make for an engaging gameplay experience.