If you are training for a marathon, go for it...otherwise???

I mowed a half acre of grass as a kid with a gas rotary mower and thought it was work. I have a garden tractor now. I suppose it depends on how you feel about exercise.

-Deerslayer

1/2 an acre is an awful lot of area for a reel
mower to handler. I use a reel mower on a much
smaller area and I have to go over it twice to
get a nice fairly even looking cut and invariably
at some point in the season the grass just gets
too thick and I switch back to a gas mower.
Reel mowers are much more pleasant to use
than gas mowers but I don't know if it'd
be worth it on that much grass.

That is a lot of grass to push through. The people who push their reels really do love their results, though. Have you considered building a patio, deck, pathways, gazebo, arbor, flower garden, zen garden, hedges, etc.?

Am I crazy or is it doable?

Yes you are crazy if you think you can do this.

For those who have compared the two, what is the difference (in terms of effort) between a reel mower and a cheaper push mower that doesn't move on its own?

I use a cheap Weed Eater mower I got from Home Depot. It doesn't push itself or anything like that. I don't find it too difficult at all. In fact, I like the fact that I am getting a bit of exercise. I have used a mower that pushes itself and haven't found it all that much easier.

I mow about 15,000 sq ft with a Scott's 20" reel mower. It's not crazy if you have the time and want a lot of exercise. I'm not one who can consistently exercise by using a treadmill, etc., it's too boring. So I "mowercise" for about 20 minutes a day, 5 days a week. I divide the lawn in sections and mow a section each day, about a three day rotation. It will not mow high grass or weeds so you need to stay after it. It's also nice to get a chore done and get some exercise at the same time. Occasionally I get lazy and let things go and have to use the power mower to catch up.
Rutgers, I have used both a push mower and the reel. If a reel is setup properly (sharp and calibrated) it is not hard to push. Plus you're pushing 30 lbs vs 80 lbs or more with a power mower.
They even make reel mowers with extra weights on the handles for even more exercise if you're really nuts. :)
These guys are right though bobbob, for half an acre, moving at a quick pace, you're looking at 20-30 minutes a day, 1.5 -2 hours a week. Great exercise though.

I just took the Scott's 20" reel mower out of my Amazon cart. Thanks for all the input.

I would kind of like to see my neighbors' expressions when they saw me pushing a reel mower. They're not big on mowerciseing.