Oh good, maybe you can explain why reel mowers do such a terrible looking job?
On the contrary, reel mowers do a better-looking job than rotary ones if you do it right. All the professional turf/greens managers use riding reel mowers, not rotary mowers, because of the superior cut. The cut is healthier for the lawn, too.
As others have said, part of doing it right is regular mowing. If you've let your grass grow into a forest and almost go to seed, then you might have to mow a couple times to get it back to looking normal. I normally mow once a week during the growing season and it looks fine. Regular mowing is better for your lawn's health, too: all the experts will tell you that you shouldn't be removing more than a third of the grass blade with each cutting. If you cut your grass down to 2 inches but every time you mow it's grown to over 5 inches, that's a great way to end up with a dying lawn, regardless of what kind of mower you're using.
Your proposed vicious cycle makes no sense; if your neighbors can't be bothered to mow their lawn more than once a month that's their problem, not their mower's.
Sargent Duck wrote:
If you have a *bigger* lawn (yet to small for a lawn tractor) a self-propelled push mower would be a huge time and energy saver. As well, reel-mowers are pretty useless in thick grass or even damp. At my old house, our front lawn got full sun but our side lawn was shaded with some nearby springs, so that it was always damp. The grass would always be twice as high as the front lawn. Or if your lawn has a high amount of weeds, those can be tough to cut through as well.
On size: it's possible that there's a range of lawn sizes where a self-propelled mower makes sense, but from my vantage point (admittedly limited experience with self-propelled mowers) I don't see it. If you're mowing regularly, pushing a manual reel mower really isn't much more work than just walking behind the mower. The real problem is time. But the cutting swath on most self-propelled push mowers is only ~3 inches wider than on a manual reel mower, and unless you propose to go jogging with your self-propelled mower (I guess some have listed top speeds of 6mph, so you could if you wanted to) you're not really moving much faster- a regular walking speed is best either way. So I don't know that you save all that much time, unless you mow considerably less frequently with your gas mower- which is possible but again is bad for your lawn. In sum, if your lawn is over a half-acre I think you need either a robot mower, a tractor/riding mower, or (probably better) a rethink of your landscaping, not a self-propelled push mower.
Some reel mowers (probably incl. mine) aren't good with the very thickest species of grasses, but there are ones (including the Fiskars one anotherengineer linked above) that handle any variety just fine. As far as dampness, I do prefer to mow when it's dry, but a regular weekly trim isn't bad when it's wet. The longer it is the more important it is to have it dry. (I do live in a fairly dry climate, and being "damp" from "nearby springs" sounds like marshes rather than lawns to me.) Weed-wise, it's certainly true that a manual mower won't do the job of a field and brush mower and cut down swaths of 8" weeds. But mowing regularly helps keep weeds down too, a reel mower will do fine with many kinds of small weeds, and for many larger weeds just cutting them with a rotary mower would just result in them springing right back up anyways- gotta pull the root out or spray.