Your second paragraph lists a bunch of aircraft all perfectly suited to the task you describe....expand the argument and you see the issue....
I own the Pitts and now want to use your Tiger Moth or perhaps some STOL Cub. All single engine, all tail draggers, in the UK tell me how I do that.
Those of us who have access to any aircraft, particularly those less commonly available to infrequent or wannabe pilots should make more effort to enable the "experience". Hopefully this means being overt in offering rides. Let the new people get bit not only by the flying bug, but many bites by different species of the bug. Show them that's there's more out there than just a 172 or PA-28. Sure, those are adequate planes, and maybe are their end objective, but allow a more broad experience for more pilots.
In the larger picture, new pilots, who are bitten by the bug beyond the 172/PA-28 should be mentored into seeking out flying opportunities in these other types. If there is a demand, a supply will make itself available. If people want to learn to fly in a Citabria, and enough of them seek this out, someone will make the plane available. If the club has one, and it never moves, they'll get rid of it.
More directly here, we experienced types should promote types more, and generalize and knock some types less. Being airborne is excellent, and the objective. I can make being airborne in a C-150, a 172 taildragger, a Super Cub on skis, a 180 on floats, an IFR 182RG, a glass cockpit 182 amphibian, or a flying boat each an excellent experience, though each in it's own way. Others here could delight me in a sailplane, a light jet, or a very light aircraft, or a high performance single. We do not advance our collective objective in promoting aviation by allowing newcomers to think of some aircraft as unworthy - they do not know the difference, so why prejudice them early?
If you're flying, even in a well worn 150, you're flying, and showing the interest, and we're happy to have you! If you grow with the 150 over the years, or trade up, delightful, keep flying.