Encoding of digital data stream to RF signal is difficult. Decoding a complex RF signal from amongst numerous conflicting signals, EMF, noise sources, etc is extremely difficult. To create a successful LTE chip requires GHz RF engineering skills (which are very rare) and then massive amounts of DSP programming (which are also pretty rare).
The only way to acquire the required skills is to work in the field at an established vendor's R&D lab. There is no way that a hacker in a spare room can acquire the required skills. Besides you need a couple of $M for test equipment and suitable environment. As for startups, they would need to poach talent from an established LTE manufacturer and pretty much start from scratch. VCs don't like those sorts of risks.