Speaking as a classical musician primarily, classical musicians not being able to groove is not related at all to the reliance on sheet music: groove is just not as high of a priority for most classical musicians (it should be much higher priority, especially for baroque and classical period music, but that’s another debate) and things like tone, intonation, and phrasing are generally the things people focus on most in the practice room. Also, if you aren’t familiar with swing music, can one actually swing regardless?
Being able to read sheet music is not an indication of one’s ability to groove: big bands are extremely reliant on sheet music and I doubt anyone would say that Basie’s or Ellington’s bands couldn’t swing. Yes, swing and groove and other musical aspects that came from an aural musical tradition are somewhat nebulous and are ultimately not best communicated through western musical notation, but that doesn’t mean people who read sheet music can’t play in those styles.
Sheet music, as a medium, is just a vehicle to communicate a composer’s/arranger’s musical intentions, and it is imperfect and weird in some places due to it being hacked together through centuries and centuries of minor changes as different composers started doing things that the then-contemporary system couldn’t handle, but right now it’s still the most effective vehicle through which we can communicate musical ideas in many circumstances.
I’ll leave this video here, which goes a little off the rails at times, but it provides a quick history of western music notation and why many proposed “fixes” to it actually have more drawbacks than the current system.