Qualcomm spends around 5.5 Billion every year in R&D or 23% of net sales. For comparison, apple spends a paltry 2.2% of its net sales on R&D. Dry up Qualcomm's net sales and the R&D will dry up too.
All the most crucial wireless patents (the really fundamental ones) have already expired. Why doesn't Apple design another, competing system around Qualcomm's patents and license it for free? The answer is that it takes a decade and tens of Billions of dollars.
Apple has the money, but it's cheaper to work the courts over so they pay less. If Apple were the ones who built 4G, you can be very sure they'd be charging at least as much as Qualcomm.
Remember, Apple thought the look of their iphone was worth $40 per device when suing Samsung, but now they think the actual technology to make it work isn't even worth $10 per device. If Qualcomm were making the same profit margins (relative to R&D) as Apple, they'd have to go from $10 per device to $100.
I'm not a Qualcomm fan (or any big corporation for that matter), but if we were making a list of price gouging companies, I think there are a lot of companies that should be getting fined and regulated (especially Apple) before Qualcomm.