Not simple. Conclusions wrong
TDD can be LESS efficient. It just can work (more slowly) in less spectrum. Also FDD can be cheaper to implement.
Uplink needs lower symbol rate as client power is more limited than Base Station. Thus even at a 8:1 ratio of download vs upload (a reasonable factor) the uplink needs about the same spectrum.
This means if you use a single unpaired channel your receiver is potentially de-sensed by other nearby modems and the available download speed on average less than 1/2 the FDD paired spectrum. You need guard time between the half duplex Transmit and Receive, reducing efficiency.
TDD will always have higher latency too.
FDD is the more efficient cheaper solution. TDD is only of value to use up odd chunks of spectrum. WiMax had it as it was Intel's concept of outdoor WiFi, hence they stuck it in the LTE spec later to satisfy the small number of operators that would want it.