Do we have any practical uses of onomatopoeia in contemporary English? I can not claim to have read many materials, but I have to confess I have rarely seen it used a lot.
Each onomatopoeic word is its own entity. Asking whether there are any practical uses for onomatopoeia is similar to asking whether there are any practical uses for words ending in f. You have to evaluate each word on a case-by-case basis.
Here is a list of some onomatopoeic words (from here):
Buzz, Beep, Whirr, Click, Clack, Clunk, Clatter, Clink, Achoo, Ahem, Fizz, Bah, Bump, Bam, Bang, Bash, Puff, Bawl, Boing, Bong, Bonk, Boo, Varoom, vroom, Bubble, Whoosh, Slurp, Wham, Biff, Pow, Snore, Swish, Swoosh, Blare, Blurt, Boing, Boink, Boom, Slurch, Clank, Clatter, Click, Ring, Ting, Honk, Jingle, Toot, Hum, Thud, Tick-tock, Cluck, Poof, Crackle, Ding, Hiccup, Crunch, Eek, Flick, Ping, Plop, Zap, Zing, Zip, Zoom
Buzz, beep, honk, plop (and so on) are perfectly normal, commonly-used English words. These words can be any type of lexical category, and can be just as useful as any other type of word.
You can say that cuckoo is an onomatopoeic word, or that is an onomatopoeia.
Apart from using onomatopoeia to mean that a word is formed from the sound it describes, or to refer to the use of such words for rhetorical effect, I don't think you usually use that word.
[Reference: the New Oxford American Dictionary.]