But the fact remains that they usually don't touch the heart of the game and merely provide the framework and tools the game designer can work with.
No... Sorry to be blunt, but it's obvious that you've never actually worked with a large team of professional game developers, because that's not how things work out in the real world.
Even the best game designer can't sit down and design exactly how every single mechanic in the game will function from button input to frame-by-frame changes in the game state. There's an initial idea with some guideance for how it should be implemented, this is produced, and then refined over time. It usually will not exactly match the idea that the designer had in mind, and/or it will demonstrate why the designer's original idea is lacking and needs refinement. These refinements will be created both independently and collaboratively by everyone involved in that particular area, which will involve the game designers (there may be general ones, and specialists -- e.g. combat designers, level designers, mechanic designers, etc) the artists (e.g. environment, character animation, concept, etc) and the programmers (e.g. general engine/technology, general game mechanics, and specialists like animation programmers, etc). If someone on the team is just a passive tool to be used to implement specifications to the letter, then they belong at a finance company, not a games studio.
The best designers are the ones who can implement their own ideas and thus keep the feedback loop very tight.
Often, a gameplay programmer with some specialty -- e.g. third person movement controllers, or weapon animation controllers, or AI navigation and planning systems, or multi-character interaction systems -- will have a lot more creative insight into their particular speciality than the game designer does. When trying to implement a designer's abstract ideas, these programmers will internally have to iterate on their implementations many times, and many of the small nuances that separate a good mechanic from a great mechanic will be injected by these programmer's own creativity independently from the game designer's overall vision. In this sense, the guy working on the "third person movement controller" may be a programmer and a "movement designer" at the same time -- and the same goes for the animators; their creativity and skills may inject new possibilities into the implementation which were unimagined by the original designer, and they may reshape the game for the better. A good designer will be receptive of the inputs of all the creative people on the team, and not just dictate that everyone stick to the original GDD to the letter. In the real world, GDD's are evolving documents that change as the game changes.
Often the high-level game designer will deliberately be vague in areas that are not his speciality to allow other designers on the team enough freedom to make their contributions great, because the high level designer is not necessarily experienced at creating the nuances in every single minute aspect of the game.
And if the game designer is REALLY good at his job, they shouldn't meddle with his process besides telling him what limitations he's working with.
I have seen several times where several variations on a game mechanic have been developed, including one which was a to-the-letter implementations of the designers words, but the latter one not shipped. In many cases, the designer has stuck to his opinion of the original idea, thinking it was superior, while everyone in play-testing felt that one of the other variations was more fun.
This designer, being a particularly good one, possessed humility (an important trait) so he compromised his own vision in order to produce a game that everyone else found to be more fun, rather that one he felt to be pure to his original imagination of the final game.
I've also seen the reverse, where a designer used his connections with management to work in a dictatorial style, where he would make changes to the game as he saw fit, regardless of the creative input of others... and the game suffered for it. Games are made by dozens of different specialists, you'd be stupid not to be receptive of their feedback.
Collaboration is not "meddling"... Collaboration is how you work with a team. A designer who can't collaborate, because they accuse people of "meddling" is not one that people will be able to work with.