It's like giving someone a longer jail sentence for having a blue aura instead of a pink one.
Because, for instance, accuracy in judgment of sincerity is a basic requirement of getting through any day for any human. In other words, we can certainly judge it accurately enough for many purposes.
Judgement of sincerity is woven into the entirety of court procedures. Why would you exclude this additional relevant data point regarding sincerity of allocution?
"Gee, I'm so sorry I drove drunk, please give me a lower sentence" is so transparently self-interested it should be discarded as evidence.
You should not incentivise people to lie, or give a specific answer.
Nor should you incentivise innocent people to proclaim their guilt