For those not familiar with the period, Tyndale was executed during the reign of Henry VIII, while England was still at least nominally a Catholic nation (Henry's relationship with Catholicism is complicated). At that time Catholicism was opposed to translations of the Bible into local languages and translation was a politically and theologically charged issue. In this case, Tyndale translated certain terms in such a way as to undermine various Catholic principles and doctrines. For example using the term Congregation, implying the Bible was referring in certain passages to the Christian community as a whole, instead of the term Church which was associated specifically with the institutions of Catholicism.

King James was a protestant ruling about 70 years later, so had no problem with an English language translation, and in fact this was an opportunity to cement the basic language of protestant Biblical interpretation in the minds of the English people.

If you're rich or powerful and don't believe it would be anathema. Letting just anyone read that ...