Why is there a flap allophone of /t/ but not of /k/ or /p/?

Question

In English, there are three (phonemic) voiceless stops: /t/, /k/, /p/. In most if not all American accents, a /t/ between vowels (the first of which is usually stressed and the second unstressed) is pronounced as a flap--the alveolar flap/tap. So we say [ɾ] is an allophone of /t/. English does not have phonemic ɾ but phonetically every (well, not every but most) consonant can occur in English.
The /t/ is prone to becoming flap but I haven't seen that happen to other voiceless stops like /k/ and /p/ when they are between vowels. Is there any reason why it only happens to /t/ in English?

GArthurBrown · Accepted Answer

I'm going to propose that this phenomenon has nothing to do with voiceless stops. I think it's worth pointing out that [ɾ] is an allophone of the voiced /d/ in at least as many accents as [ɾ] is an allophone of /t/. Though, I suspect that /d/ is flapped/tapped in more accents for the reason that Brits so commonly ask why Americans/Canadians/Australians use a D in place of T, which implies they perceive [ɾ] an an allophone of /d/ but not /t/.
(Wikipedia)

In North American English, /d/, the voiced counterpart of /t/, in such
positions is also frequently pronounced as a flap, making pairs of
words like latter and ladder sound similar or identical.

Which might lead one to conclude that flaps/taps are not a product of voicelessness or plosivity at all. /t/ and /d/ are realized as a flap/tap in some contexts because these sounds are all alveolar, while /k/ and /p/ are velar and bilabial respectively. Though there are apparently velar taps and bilabial flaps in existence, these are exceedingly rare, to the point there is not even an IPA symbol for the velar tap, and the bilabial flap only exists (primarily as an allophone of a labiodental flap) in a small group of Central African Languages. This might imply that ease of articulation is a factor in why these sounds are not as widespread as alveolar flaps. (Note: flaps/taps can be voiced or unvoiced.)

JeffUK · Answer

"A flap (also: alveolar tap or single tap trill) is a term that describes a speech sound produced when the tongue quickly and briefly makes contact with the ridge behind the upper front teeth. " https://dailycues.com/learn/iqpedia/pages/flap/
I don't think it's possible to pronounce 'k' or 'p' whilst simultaneously touching the ridge behind your teeth with your tongue.

Decapitated Soul · Answer

As Prof John Lawler said in a comment:

The velar and labial articulators are flat and close over an area. They can slap (as in velar ingressives or loud kisses) but they can't flap (except in a trill); the dental/alveolar articulators, however, are different and the tonguetip is easy to tap. It's all architecture.

Why is there a flap allophone of /t/ but not of /k/ or /p/?

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