Miki, the reasons why I have chosen to UM most of my stamps are for the same reasons Michele mentioned earlier. UM stamps are less cumbersom to store/organize. I find them very easy to use, and less costly than wood mounted stamps too.
You bring up two good points though. Convenience and cost are always worth looking into!
Convienence wise... I have hundreds of UM stamps stored in a single filing crate. Each mounted on a sheet that shows the picture of the image, and the company name. If I know the name, that is. I say that because some of my UM stamps I inherited or received in RAKs and no accompaning info came with them. I can easily take this entire crate with me from my art studio to the dining room, the TV viewing areas, or even to my car if I want to take a lot of stamps with me somewhere. Other stampers I know use a 3-ring binder type system that makes it easy to travel with. I think that's what kind Jeanne mentioned she uses. So personally UM's are more convenient for me. There's no way I could easily move around very many wood mounted stamps.
I'm not a super strick about my storage/organization though. I also have some UM's stored in CD cases because that's the way they came and it's easier to just keep them there. The casset cases are thin enough to store easily enough in the same filing folders as my others. And my CTMH stamps come in little plastic sleeve type pockets. So I keep them in their original packaging too. Again, mainly because these sleeves fit nicely into the file folders.
I still have some stamps that don't get stored that way though. Mainly my fonts. If they come on a block, I keep them on the blocks. It's just easier for me to be lazy and store them in baskets rather than take the time to unmount them.

Maybe some day I'll get real industrious and do those too. But I honestly doubt it.
The big chunky foam stamps like the ones I usually use with acrylic paints (puchased at most any department store) -- those are also tossed into baskets instead of messing around with unmounting them. I'm not even sure of how to go about unmounting that kind. I guess it may be the same microwave thing... but I don't know that for sure.
As for expense: In many cases I can get two or three times as many unmounted stamps for the price of a wooden one. However, that varies from company to company as well as the type of unmounted. Clear acrylic stamps are (usually) a little more expensive than others. Stamps bought in rubber sheets or plates are definately cheaper!
I use a glue that adds a repositionable layer for the backing on my rubber ones. I know many stampers use the EZ mount (like Michele). But I honestly prefer not to have the cushiony stuff. I think I may be unusual in that though. I do a whole mess of stamps at one time. Because I'm not crazy about doing the whole glue/drying thing very often. I'm rather impatient with that.

That's one of the reasons I agree with you Miki - the acrylic stamps and the wood blocked stamps are great for quick starts because you don't have to do anything to prepare them before you can start using them! I tend to use my wood blocked stamps for quit sometime before I finally get around to UM-ing them. Lazy, lazy, lazy I am. For me the glue is very econimical... I don't know about the cost of EZ mount. That might add up to more $$$'s. Maybe Michele and others can shed some light on the expense of EZ mount.
There is the additional cost of acrylic blocks for most stampers too. I have several sizes already. And I guess they may have seemed a bit expensive at the time. But they are a better deal in the long run. Mostly storage wise again. But I haven't broken down to buy me a big one yet. So if I'm stamping with a larger rubber image I'll use an old CD case for my block... or nothing except my hands. I find both are good options. Plus there's no additional cost either. I will also sometimes use a CD case if I'm wanting to do several smaller images at once. That way I can see where my placement is going to be before I do the stamping. This is a super fast/easy/inexpensive way to do mailart on envi's.
TIP: For unmounted fonts -- Use a ruler and draw lines with a permanent marker onto your clear CD case. Then use the CD case as your block. This will make it easier to get letter stamps in a straight line and spaced however you want them.

(Or spend the extra $$ to buy a clear acrylic block with the lines already on it. -- A luxury I still haven't afforded myself with.)
Conclusion: For me UM is more convenient, less expensive, better to organize/manage, and just as easy to use... sometimes easier when I can see through them. And that, my friend Miki, is why I choose to unmount most of my stamps.