Though this may reflect your experience, it is certainly far from being the absolute statement you make it out to be.
You can indeed use any medium to record tons of useless images.
Film expenses are entirely dependent on how much you shoot, and if you factor in re-sale value of film gear, cost of home developing, depreciation of digital gear, it may even work out to be cheaper. The OP indicated quite clearly that he intends on this being a new experience to him, and he is approaching it with the right mindset. It can be self correcting, you can burn through film if you need to, but if you finish a roll...well...no more roll.
In regards to choice of medium and personal improvement, I think that you will find many here have seen their work improve after picking up one specific camera or another. It's certainly not the camera that's making them better, but the mindset directly behind the viewfinder. It can and does change depending on what type of gear you are using. If you are chimping, you're not seeing, and a film camera easily takes care of that.
What I was alluding to is that one shutter press (in single mode) equates to one exposure regardless of the recording medium, film or digital. Seeing, framing, and exposing requires discipline regardless of the medium, and changing media is NOT going to change the amount of discipline one brings to the camera. Merely that the medium
allows one to machine-gun exposures doesn't mean that one
must do that. You can (and should) bring the same discipline that photographers seem to think that film brings them to digital. There's no reason not to. That said, the more frequently you shoot, the better (hopefully) your images become. (Note that I suggest that the more frequently you shoot... and that does NOT equate to quantity of images... but rather quality.)
Film can have a different visual quality than digital, and as Takkun said, you should shoot film for the properties of film.
I've noticed that different cameras inspire different shots, the same with lenses. My Olympus makes me shoot more "incidental" shots, stupid things that grab me. My Pentax, for some reason, makes me want to reach for bellows. What would a RF drive me towards? What would film? Thats the question. There must be a draw, after reading through these forums there are people out there who feel it. Why don't all of you shoot with modern, feature filled, DSLRs? Easier, less work for results, etc... Perhaps I just want to try something different, since that always makes me better at what I do.
Cameras don't "make" a photographer do anything. As I said before, a camera is a box for film (or a sensor) with a lens for focusing light. Despite what you might read in advertising hype, they are nothing more and nothing less.
What they do have, and what differentiates them from one another are their ergonomics, their feature sets, and the system behind them that allows them to be more versatile.
Over the past forty-something years, I've used just about every style and type of camera to shoot all kinds of subjects in all kinds of circumstances. I've been the "this camera system for this job, and that camera system for that job" route. I've shot view cameras, press cameras, rangefinders, SLRs, and digital of various kinds. In the digital world, the feature-laden DSLRs are now the "thing," although here many members tout the value of film and rangefinders. Because of our individual preference for design and "feel" of cameras, we gravitate to one brand over another.
What I HAVE discovered in
my journey is that, just as in sports, knowing and performing the fundamentals
every time is what gets the job done. It's nice that the camera can do thing for you, but if you know what
you want it to do, all those features become an impediment to
you controlling the camera to make the image
you want instead of making the image that whoever programmed the camera told it to make.
And that comes back to self-discipline; knowing and understanding your craft thoroughly, and making those decisions for yourself rather than allowing your equipment to do it. I became more and more dissatisfied with the feature-laden modern cameras as it has become more and more difficult to override to get them to "manual." So I returned to Leica (both film and digital) as my ONLY system as it can do whatever I need for it to do in commercial service. It may not be as fast or convenient in some situations as a DSLR, but I can still do the job with them and do it quite handily.
Actually, I kind of take that back... Cameras have a mystique.
So, I'd suggest that "Mystique" doesn't really come from the cameras at all, but comes from photographers projecting that onto the box that contains the film. They'll all get the job done, it's just that some "feel" better, are "easier" to use, or have wider systems to support them.