WiMAX also has an FDD mode so you're argument concerning that doesn't hold. But in anycase LTE is better so it doesn't matter. LTE is better for the following reasons:
1) 1ms subframe duration compared to 5ms subframe duration in WiMAX means that LTE can offer better frequency selective scheduling, which means higher throughputs.
2) LTE has more redundant coding of PDCCH compared to WiMAX control channels, so LTE should tolerate interference and drop calls less than WiMAX. LTE in general seems to have better thought out coding.
3) LTE was designed with a lot more input from global telecoms providers, so interoperability across borders will be better.
There are other reasons but these are the main ones. So LTE is a "good thing".