You are definitely taking creativity away from the players with the version of wild shape in the current playtest. It doesn't take any creativity to say "I use wild shape" when, for the first tier of play there is one option and set of stats, or at higher levels the only choice is "walk, swim, or fly?" The "freedom to flavour" is simply the freedom to think of a specific animal for your generic template...or not. I suspect many players won't even bother unless prompted by the DM.
The current system does not require "encyclopedic knowledge," it requires players to either do a little research beforehand (ideal), open a monster manual, or do a quick google. Or just say what they want to transform into and let the DM handle it. I teach new players a lot, and when they are choosing druid I ask them to take a few minutes to come up with their favourite wild shape options. Some players leave it at that, and some get really into it and spend hours, because it's fun for them.
You can't have much creativity when you have one tool available, which is what the current proposal offers. Which you basically acknowledge by then adding in "there should be scope for more abilities and mechanical customisation in wild shape than that currently shown." Okay, now we're back to where I started, which is that the more we add complexity to the template, the more it starts to look like what we currently have. Except generic.
1. We've previously discussed this a lot, but no, I don't think it is bad that druids have options that other classes don't. Different classes do different things, inside and outside of combat. I don't think martial classes are suffering in 5e. I think druids, aside from moon druids, are considered a pretty average class, and 90% of the discussion on how to "fix" (i.e. nerf) druids is a discussion about that one sub-class.
2. So barbarians? As I've previously discussed at length, with math, I think the current method of druid tanking ("damage sponge") is different from other methods of tanking and that makes it interesting. It's just unbalanced at low levels.
3. As I discussed previously, if you are going to have templates, the player needs to still be required to come up with a specific animal form or the whole exercise is generic and boring. "I assume water form and swim across" is not very fun or imaginative. Right now, the character has to do some interesting thinking - "what would my character know? What specific animal would be most useful here? Oh, I want to swim underwater and open a grate, so maybe...an octopus? Or an otter?"
4. I agree - I've already argued that elemental forms need to be much more robust than what is in the playtest, and have never made sense for moon druids.