How much do you think I think Sprint spent on WiMax? If it wasn't very much then why was their LTE network so shitty for so long?
I was a Sprint early adopter when they were the first ones to launch a nationwide CDMA network and stuck with them for years even when it became clear that 3G GSM was technically superior (no simultaneous voice and data over CDMA). But I finally had to switch when they dragged their heels on deploying 4G LTE.
WiMax is why sprint didn't have an LTE network for so long, my market (Seattle) didn't get LTE until Q2 2013 in any form, and it wasn't even fully turned up until like Q4 2014, if not into early 2015.
I don't have a dollar estimate though. I know that having to do site development for all those non-shared sites, was very very expensive. I also know that Sprint made other network upgrades too in that time.
I disagree with your assertion however that GSM is superior to CDMA - GSM has the advantage of being more extensible, because its a collection of loosely coupled network elements working in tandem, but in terms of network construction CDMA is much more forgiving for poor deployment engineering, and offers (in my opinion) much better audio quality compared to GSM. CDMA also has one more advantage for the future, you can build a market out on it, and put all the sites on a single CDMA carrier (frequency), allowing you to more aggressively reallocate your spectrum to other uses (like LTE).
The reasons Sprints LTE network sucks is spectrum, in most of their markets, they don't have enough spectrum in the right band (1900 MHz PCS Block) to cram enough bandwidth into a macro site, meaning you have to do things like densification, which Sprint is very well positioned for with spectrum, but poorly positioned for in customer counts - its this math that really leads me to believe that there is no room for 4 competitive national networks, there are just not enough customers to pay the bills and keep the lights on.
None of the efficiency of CDMA matters from a customer experience standpoint. If it couldn't do simultaneous voice and data then it was inferior technology.
I was a Sprint early adopter when they were the first ones to launch a nationwide CDMA network and stuck with them for years even when it became clear that 3G GSM was technically superior (no simultaneous voice and data over CDMA). But I finally had to switch when they dragged their heels on deploying 4G LTE.