I've been tempted to get a "human-powered" reel mower (as a second mower), but haven't.

I grew up pushing one of those cast-iron models over a large lawn featuring three terraced levels in front of the house. Not fun! On the other hand, I've seen and (briefly) pushed more modern lightweight manual mowers, and they're quite a bit easier to use.

However, they're useless if you let the grass grow too long, and/or if you have weeds standing higher than about 4-6 inches scattered across your lawn. Reel mowers (even the power models) don't cut high growth, they just bend it over. A rotary will cut anything, but reel mowers aren't very practical except for golf greens and very-well-tended, weed-free lawns. Of course, when use in those optimum circonstances, reel mowers produce a superior cut. In the context of a rough-and-ready yard where different grasses and weeds are mixed, and where you sometimes let it grow too long, I think you really need a rotary power mower.

Maybe you can have a non-power reel mower as a second choice, and use it when the lawn is already fairly trim and you want the exercise, or to save gas and avoid polluting. And, if you're really scrupulous about cutting every single weekend, or maybe even more often, maybe you can keep the lawn in good enough shape not to need the power mower for weeks or months at a time. But once you let it grow too much, the push/reel mower will be much more difficult to operate and may fail to do the job at all.

As far as collecting clippings for mulch is concerned, bags or other such catching devices are available for reel as well as rotary mowers, and if you don't have such a catcher, well, that's what they make rakes for.

PS: I always used to call the non-power mower a "push" mower, but nowadays that term has come to mean a power mower that is not self-propelled. How times have changed!