It's pretty clear by the a straight reading of the rules that this should work. I want to focus on the later part of your question,
Also, am I being overbearing and unreasonable by not allowing this?
I have experience with this both as a DM and as a player, and from both I'd encourage you to not just allow this but to encourage it.
The DM experience isn't with a druid, but has to do with party communication. I had a player who was all in on the idea that the kenku race cannot say anything new and can just repeat. This was mildly amusing for a session, but after that it mostly was frustrating for the people in the party who wanted to plan and work together. (Including, actually, the player.) In my experience, the game overall is just plain more fun when the party can communicate effectively.
As a player, I have seen the opposite side. In one game, I have a druid in a party with another character who can speak with beasts, and the DM ruled a) this works when I'm in wild shape form and b) that for simplicity we can pretend that the player is translating anything important I say for the rest of the party. The key things are: yes, as above, this makes playing more fun, but also, it's not overpowered in the way you're worried about in that it doesn't really enable me to stay in beast form longer that I would otherwise, because in practice there is almost always another good reason I can't be a giant constrictor snake in the town center.
Also: hey, this is a useful combo is a perfectly normal way to get a character concept started. Sure, it may come from a "powergamer" impulse, but even that can lead to good things. Druid is perfectly thematic for the ghostwise halfling in Forgotten Realms, but as you note their tribes are often isolated — so, your character starts out with at least one interesting thing: why are they here? That's awesome — a lot of times players have even less than that to build on.
So, rather than pushing back, I'd encourage you to say "yes! that's awesome!" and ask some leading questions to build some connections and hooks into your campaign.