From what I know, you don't need any licensing to design and implement a 3G/4G/ or even 5G Modem. ( Unless you want CDMA Support ) It is the ODM or Phone Manufactures that has to take care of it. Much like you don't need a license to include H.264 decoder, not even to ship it. But you will need to pay if you decide to enable it.
>only successful cellular maker I'm aware of besides Qualcomm is MediaTek
Mediatek is awesome. By concentrating on low end, something Qualcomm doesn't want to do, they have an economy of scale for both Fabs Capacity, Design and Modem testing.
And just a note, Huawei, assuming they will Settle with Qualcomm, and Samsung both have their own Modem Implementation. These two represent close to 40% of market. And if you include Apple down the line, that is roughly 55%. Adding Mediatek, that is close to 70%. And that is excluding BBK and Xiamoi plans to make their own modem, together they represent 15% to 20%. Qualcomm doesn't have a monopoly as media likes to paint it.