sr_iyer has addressed your question substantially. When I read your question, the first composer that came to my mind was OVK as well. There is an album by TNS of OVK compositions. What a great match-up!!
While pondering your question, I thought of the following:
sr_iyer had nicely built up the kaNakku from Sarali to varnam to pallavi. And you were wondering about pre-composed music. And the biggest one of them of course is the krithis.
As Sri. Srikantan says, traditional thinking is krithis represent the rakthi bhakti sangitam. Whereas this would be rakthi kaNakku sangitam

That is on a lighter note of course, but that may point to the standard thinking on the differences in aesthetic goals of pre-composed music vs manodharma music.
Not that they can not be reconciled, I am sure people can relate to bhavam/emotion induced through music that provides for kaNakku based speed variations.
As you and sr_iyer covered, jatiswarams, tillAnas and orchestral pieces can definitely make use of these for good effect.
Here is the main point I wanted to write about as a possible direction of thinking for your question. There may actually be not that much difference in aesthetic goals between those sub-genres.
What we are basically talking about is syncopated speed variations in pre-composed music.
Manodharma aspects including niraval readily accommodate such things. What is the equivalent of niraval in pre-composed music? It is of course Sangathi. May be that is one place where chathusra-thisram type speed variation can find its place. In many thyagaraja krithis, the sangathis are built up with speed variations. You see a pattern where he sometimes speeds up the pUrvAnga while maintaining uttaranga and vice versa in other krithis or both in some krithis. They are normally 'power of 2' speed variations which are not normally syncopated. And Thyagaraja was a master at using off-beat and syncopated constructions. I do not see why chathusra-thisram type speed variation can not be accommodated in such sangathi construction. It is really not even gathi-bedam as sr_iyer observed earlier, just an illusion while still in chathusram.