I've studied linguistics fairly extensively, also constructed quite a few languages...though they're rather bad

...and here are a few problems I thought of that you might run into. Keep in mind that I'm coming from the perspective of a naturalistic conlanger, so to speak, which means that I try to construct languages like the ones on Earth.
-The resulting words might be too long. You could have really short roots, but then you have a limited number of roots, depending on what sounds you have in your language. (And BTW in most languages "bird" is a more basic word, and so more likely to be a root, than "feathered"...but who knows, maybe you could have a language based almost entirely on adjectives. Now that would be quite cool, actually!)
-Especially if the words are long, they'll wear down over time. Sounds will change, syllables will blend together...and soon the original roots won't really be distinguishable. Why doesn't this happen with scientific terms, etc. in English? I think it's probably because they're used so rarely, and also because I'd guess that they're written more than they're spoken.
-The meanings of words changes a lot over time. The word "nice" once meant "clumsy," for instance. (see
http://www.etymonline.com/index.php?term=nice&allowed_in_frame=0) Granted, that was in the 1100s...but the point is that even if your language started out with a lovely perfect roots system, in a few hundred years the meanings of many words and their original roots would seem to have very little to do with each other. In the end, what roots are associated with what meanings would be rather random.
-Speaking of your language starting out...how
would it start out with such a system? It's too neat and perfect to develop slowly and naturally, so perhaps someone created it...? This isn't so much a problem as an interesting question to think about.
In the end, I think it would be most
realistic for a language to have
some words built in this way, like the examples others gave below. To have all words, even most words, be derived this way is kind of pushing it in terms of realism. However, this is fantasy!

If you can come up for an explanation for how your language got to be so neat and tidy and how it doesn't change and mess up all the neatness, go for it! I would love to see a good explanation for this sort of language, because I think it is a secret desire in every language creator's heart to construct a wonderful, metaphorical, simple, straightforward roots-based language like this.
