Intel (Infineon) did so, chip is called SMARTi4G.
Seems like too many people here didn't get it that Intel has a ready to go LTE, HSPA, ... solution just like the competitors, there's only no LTE integration into their App.Proc. available yet...
I remember when Intel set the standard for putting WiFi in portables, which changed the industry.
They tried it again with WiMax (do you remember the WiMax portables?) But, as with Sprint, they were too...early. The industry is now standardizing on LTE which came after WiMax.
The problem with LTE is that there are so many broadcasting bands of LTE (and more that will be converted to LTE later) and even two types of LTE (TD-LTE, FD-LTE). How do you make a chip that can handle all of the present and future broadcasting bands of LTE and advanced LTE?
I think it is a typical problem of many acquisitions in the communication space done by Intel over the past 20 years - none of them worked. The most similar example was DSPC that Intel bought 15 years ago and sold several years later to Marvel at half price. Intel will try to do the same here but it will be much tougher to find a buyer because the market changed and there are not so many potential interested parties (maybe none - see TI and Freescale efforts to divest their wireless activities and ST failing venture).