Because I would want to see these two traditions actually married together. A level of Monk means you have been initiated. I would prefer to see someone delve deeper before they produce a unified, integrated expression of these things. This, incidentally, is what I would do in essentially any game. E.g. if a player took a Monk MC feat in 4e,* I would expect them to put further investment into it to make it work--perhaps a Monk PP, or some extra Monk feats, or going to multiple monasteries to study under various masters (=some rolls each time to determine progress, you will make progress but it might be slow or might be super fast), etc. Many routes to the same end; make the journey short enough so that the player can complete it well before the campaign ends, but long enough that it feels like a true achievement, something earned, not merely picked up on a lark.
Keep in mind, I used "or" and very specifically allowed for a pure-roleplay solution, one that doesn't require spending resources (levels, feats, items, etc.), and instead represents the character's journey as they learn to blend these disciplines together. I support this sort of thing wholeheartedly! I just personally prefer to see the player demonstrate the link through play.
Plus...isn't the player already getting an interaction that is probably not intended? IIRC, people have already said that Unarmored Defense simply doesn't work at all while wildshaped. It would seem to me that allowing it to work in some way, and providing multiple routes for building toward something even better, is a perfectly reasonable thing. What do you feel is lacking here?
*As opposed to starting the game as a hybrid Druid|Monk, which is very much designed to be a true blend of the two sides....and has to spend a feat to get closer to "full" from one of its two halves!
Well I'm not sure that there's a good reason why Unarmored Defense cannot be allowed. It's a class ability, Druids can still use those while Wild Shaped. As for the "must be able to physically perform" clause, I don't see how this really applies.
Can an animal move like a monk? Given that there are real world martial arts styles developed from emulating how animals move- I'm going to say probably?
Can an animal be as tough as a Barbarian? Given that the most popular Barbarian subclass literally gains powers from animal spirits, I'm going to say probably?
Now in your campaign, it appears you want the narrative to at least match the mechanics, if not trump them outright (if I misunderstood you, I apologize in advance). There is absolutely nothing wrong with this. Ideally, every choice a player makes is one that is grounded in the narrative.
However, sometimes choices that "make sense" actually hamper or hinder characters, and sometimes the best choice you can make is one that comes out of left field. While the GM can step in to make the former function, that doesn't necessarily mean that the GM should step in to police the latter- the player feels that their character is missing something, and I don't see a good reason to say to them "sorry, you can't do this because it doesn't make sense to me".
As long as it makes sense to them, that should be enough, at least that's how I think.
In discussions like these, I see a lot of people throwing around concepts like "unbalanced". In this case, the pushback seems to be that Druids are intended to have poor AC to make up for the durability of their beast forms, and somehow the game would be unbalanced if a player attempts to boost their AC.
That's like saying a Barbarian shouldn't pick up a Shield because the durability boost of Rage is predicated upon poor Barbarian AC. But they are allowed to make that choice, just as they are allowed to boost Dexterity or be judicious in the use of Reckless Attack.
You mention wanting the player to be a hybrid of Monk and Druid; unfortunately the rules don't really support that sort of thing well. There's not enough synergy between the two paths; a Druid 10 is simply a better character than a Monk 5/Druid 5 (and quite probably a Monk 10 is better as well).
Ideally, we'd have a subclass along the lines of 3.5's Fist of the Forest or the UA Druidic Avenger to blur the lines between the class archetypes- but barring 3PP, I don't see WotC doing this, so hybrid concepts are only doable with multiclassing, and each level take in one class or the other has tradeoffs that can hamper one's character concept, as I pointed out.
A Druid does not get very much use out of Martial Arts; their Wild Shape attacks are likely superior, and natural weapons are neither Monk weapons nor Unarmed Strikes, so the bonus action attack would simply lie fallow. While the other uses of Ki can come in handy, and Extra Attack is functional for Wild Shape, and Stunning Fist of course requires not using your natural weapons. And all these Monk levels mean that the Druid is not getting better Wild Shape forms to work with in the meantime.
Further, there is the loss of spells, which will be greatly felt when our Druid/Monk no longer has Wild Shape to work with, as he's now a poor Monk with the effective spell power of a Ranger! So imposing such a path on a character who just wanted better AC does not feel like a fair trade.
But that's just my opinion.
