4G's sticking point is speed. Specifically, the ITU-R IMT Advanced proposal requires several things, of which, today, are easy to meet. What wasn't easy was 100mbit peak speeds for mobile users, gigabit peak speeds for fixed users.
WiMAX in a lot of markets is not 4G, but neither is LTE in a lot of markets. In other words, a lot of markets do not, and seemingly never will, have 4G as defined by IMT Advanced. I live in a market that is LTE, is sold to me as 4G, will never meet 4G requirements.
WiMAX was developed with proposals like IMT Advanced in mind: ability to have MIMO, all IP packet switching (non-VoLTE LTE networks cannot ever qualify to be called a 4G network due to this, btw), 20mhz and higher channel widths, and spectral efficiency above a certain level (which put a lower limit on how big your modem's DSP has to be due to coding techniques), forwards and backwards compatibility of future specs, and smooth handover between heterogeneous technology (ie, tower to home femtocell and back). WiMAX's original specification (802.16e-2005, which was based on the original 802.16 spec from 2001) met the IMT Advanced requirements.
LTE was not developed from day one to do this, and did not really meet the requirements until LTE-Advanced. The original LTE specification (3GPP release 8 (2008); LTE-A was defined in release 10 (2011); LTE-A Pro was defined in release 13/14 (2016/2017); additions to LTE-A Pro for 5G (but does not meet 5G yet) were added to release 15 (2018)) fell short of the speed requirement.
What makes this all interesting is, WiMax could do fixed modems 10 years before LTE-A added it, was "true 4G" (as how ITU-R defines it now due to how everyone rushed to muddy the definition with HSPA+ and whatnot) 3 years before LTE was, and is currently the only protocol that has hope of deploying gigabit to fixed users currently (via 802.16m-2011/802.16-2012 aka WiMax 2 or WiMax-Advanced).
Also, they're trying to sell LTE as 5G, I've already seen ads saying 600/700mhz support is 5G (it is not, although it is welcome), just like how they tried to sell highest order (2x2 MIMO with dual cell and widest channels) HSPA+ as 4G (which would be more correctly be described as 3.5G, as newest spec LTE would be best described as 4.5G).