Why doesn't "bounce" rhyme with "counts"?

As John Lawler says, in practice the two words sound the same.

Rhyme used to be judged entirely by ear, but online dictionaries use rules and analysis instead. So their definition of a perfect rhyme may differ from the average person's.

If you insert a t-sound into ounce, without slowing down, you end up with. . . ounce! (And it's perfectly pronountsed!) You can separate the last two letters of counts to make the t audible, but in normal speech we don't.

Poets and lyricists use rhymes like counts/ounce with a happy disregard for the velic flap. Wordsworth, Browning and Tennyson used near rhymes like love-move, suns-bronze-once and creature-nature, which no rhyming dictionary would allow.

Walker's Rhyming Dictionary of the English Language - "devised for the rhymer, not the phonetician" - is a 'backwards dictionary'. It badly needs updating and is tricky to master but it does at least leave it to the reader to decide which word suits his/her purpose.

Rhyme is based on phonemic form. "Counts" is phonemically /kawnts/, while "bounce" is /bawns/. They don't end the same way, so they don't rhyme.

The pronunciations of /ns/ and /nts/, as opposed to the phonemics, overlap, since the difference between the phonetic [ns] and [nts] is a rather delicate matter of timing the dropping of the velum to let air pass out the nose. The two words can end the same in pronunciation, but phonemes govern perception. The ends of the words still sound different.