I think you can have one that is more obviously done this way than English is, though. Even English words are built from other words, put together to make a new meaning, but English is such a mash of languages, French, Saxon, Greek, Latin, and so on, that most of the beginning words aren't ones we know, since we don't know Greek, Latin, etcetera. Kindergarten is a word from German, that is put together from 'child' and 'garden' and means a school for young children. 'Protagonist' is a word from Greek, and it is put together from 'first in importance' and 'actor', and means (unless otherwise defined by someone trying to expound writing theory) the most important person in a story.
From what I know (though I am by no means knowledgeable in German or any other language), German is more along the lines you're talking about than English appears to be, and I'm fairly certain that Saxon is as well. And from what I know of the huffy scientific names for everything, they often just mean things like 'night wanderer' and 'striped storer' as well as various other more boring descriptors.
So it's not an un-do-able idea. Though I agree with Kingjon that you can't have every word put together this way, as you have to have the roots to build from. Personally, I love language along these lines. It appeals to my taste for metaphors.
...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.
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.