Would this put a lot of wear on the saw?

It depends, if you are heating and binding the blade a lot then it can, if the logs aren't clean and you are cutting some soil then yes.

If the wood is clean and a little green then theoretically it will be less taxing on the blade.

Lumber is always clean and straight and that is what this saw is designed for, so wiegh the differences against that to determine the effect your wood might be having.

Not to sure what you are after, but one point for those who think this might be safer is any time you have one hand one the saw, and one hand on the wood, while running, you have a dangerous situation you need to be alert to. CSs have their issues, but if you keep both hands on the saw, you will not be cutting one of them off in most instances.

Is this a 'don't have a chainsaw, making do' thing, or a 'hey, is this a better option?' thing?

If you really, really don't want to use a chainsaw, and are willing to put in the time to build some sort of station to handle logs so that they can readily be brought to the saw/moved around, instead of carrying the saw around... maybe a radial arm saw would do the trick? I haven't any substantial experience with them, but you can get them in BIG blade sizes, and I have heard these larger, heavy duty units are less dangerous than the smaller craftsman ~10" that were very common a few decades back.

An electric miter saw? as in a chop saw that you use for angle cuts? Those blades are easily replaced and much cheaper than a new chain for your chain saw.

Is this a hand miter saw or a power saw? I would not try using a circular saw blade (skill saw, chop saw, or other) for trying to cut down a tree. Especially one attached to a machine meant to chop vertical while stationary. Green wood saws have a rake to the teeth that cuts a substantially larger kerf than the thickness of the blade. I have never seen a circular saw blade that cuts that big of a kerf compared to the blade for common arbor sizes found on construction tools.. It would have a high likelyhood of getting stuck or it could kick back. I can't imagine how awkward it would be holding a chop saw up to a tree, let alone trying to hold it firmly enough to keep it under control in the event of a kickback.

As far as cost, it doesn't seem like it is much cheaper either, unless it's the only cutting tool you own. Finding an appropriate tool really depends on location and tree size and number of trees. For a handful of trees I would get a bow saw or for smaller trees some sort of green wood hand saw. Even a hacksaw or sawzall would be fine for smaller trees. They have cheap electric chain saws that work well for light duty stuff. If you want cheap and reliable then an axe would be the best tool for the job.

I assume that you mean to process long sticks into firewood length. Circular saws don't work very well in falling wood.
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This is very common, even among those who have chainsaws. I do it, my brother does it, my friend Felix does it... It's a speed thing. Very quick, once you get the knack. No fumes. We all still have 10 digits. I prefer radial arm saws. They come up for free regularly. More power and a long stroke.

I did this last fall. I stacked up some palettes and put a chop saw on that. I cut lots of trimmed branches to about 6-7" (what I need for my 6" RMH).

I couldn't do stuff that was too thick - still have to use the chainsaw for that. Maybe 5" thick is too much. And you do have to watch for pieces kicking out if they aren't straight and aligned against the back wall. But it was a heck of a lot faster and resulted in a nice pile.

Most of it still needed to be split at least once.

I'm going to be setting this up again soon, only on the same side of the house as the storage racks I built (out of palettes) so I don't have to carry the finished wood as far.

Yep.....this seems to work well so far. We have two cheap (under $100.00) chop saws on which I replaced the cutting wheel with a ripping blade, each saw in its own location. By using a tractor with a rear-mounted PTO-driven generator under a platform, the saw can be positioned on the platform and the whole shebang taken out to far reaches on the property. Instant "chopping mill" for 6" or less rounds for firewood.

Just an FYI. They make blades specifically for green wood(well, wet really): http://www.tools-plus.com/hitachi-115300.html?gclid=COTEpf-W4csCFUQ9gQodQ3oDcA That's far from the only blade, many companies make them.