Since wireless radios are half duplex, do they divide their time up evenly 50/50 in Tx mode and Rx mode? If so, wouldn't that halve the effective throughput? And yet we are able to achieve throughput greater than 50% of the theoretical link rate.
Half duplex implies that there is a shared medium (in this case the radio spectrum) that is capable to transport one data flow.
Usually when an host wants to transmit over a shared medium has to run an algorithm to ensure he is the only one that is transmitting to avoid collisions. In the wi-fi world the alghoritm is the CSMA/CA.
When an host "wins" the channel he transmits at the full bandwidth of the channel.
What you've described better fits in the Time division multiplexing (TDM) that is not really an access method but is a multiplexing one.