The issue is probably all the contaminants in human poo, especially medical: anti-bacterials, hormones, radioactive tracers. Maybe it isn't so much purifying the phosphate that matters, but removing components that would be bad to recirculate into our food chain.
High temperature composting deal with the most common problems anyways, and you preserve the nutrients rather than burn them up. The biggest problem is how bad water waste management systems are at producing fertiziler, the wide spread idea that it's ok to pollute our waste water with what ever, making it unusable for composte is not healthy. I do not think burning it can solve more than a tiny part of that problem.
