I recall seeing recommendations, in multiple Halachic discussions, that someone who's reciting a Scripturally-derived prayer alone that normally requires a minyan, e.g. the 13 Attributes of Mercy, one should say it with the trop. Apparently, this feature converts the recitation from prayer into Torah learning, so one isn't incorrectly subverting the minyan rule.
On the other hand, I also recall learning in school to recite the Keriat Shema with the trop as a standard practice.
Is my understanding of the function of trop in the first case correct?
Is it true that reciting Keriat Shema is best done with the trop?
If so, why doesn't the same function similarly de-prayerify the Keriat Shema?