Even if you can achieve comparable performance on N concurrent TLS connections (which I actually think you can), you have a high additional cost of establishing

Even if you can achieve comparable performance on N concurrent TLS connections (which I actually think you can), you have a high additional cost of establishing those N connections. For a lot of systems the TLS handshake is the most expensive part of an operation. Reducing the amount of TLS handshakes by N can literally reduce cost by up to N in those systems.