They did not have enough British soldiers. While the British Army had effective soldiers in it, they were not treated well. They were enlisted for a very long time- often life. They were not looked after by their officers. Any able-bodied young man who could find something better to do would try to do so. Efforts were made in 1775 to recruit more by limiting enlistment to three years or the duration of the revolt, and some gains were made by pardoning criminals in exchange for service. But it was still not enough.
The British had some connections to the Germanies already ( the Hanoverians were from Hanover, and George III even still served as an elector there). The German rulers also were a pretty greedy bunch, with palaces to keep up and total authority over their subjects, and so their impressment and sale of soldiers could be more ruthless and effective. The Landgrave of Hesse-Cassel had hired his soldiers to England five times before ( some were at the Battle of Culloden) and was happy to do so again. He agreed in 1775 to send an initial 12,000, later another 5,000. Considering the population of his principality was about 300,000, this seems a big burden. But the Prince of Anhalt-Zerbst had 20,000 in his, a province already blighted by war and famine, and yet still agreed to send 1,000 soldiers (though he was of such a dubious character that the British refused to pay him until the soldiers actually appeared). The Duke of Brunswick asked for and got a famous "bloood-money" agreement in his contract, paying him a lump sum for every soldier killed or captured, and for every three that were wounded. One conscript called the Landgrave "a seller of human souls".
The hiring out of mercenaries was disliked not only by German intellectuals hoping for a bit of the Enlightenment to come their way (like Schiller) but British politicians like Edmund Burke, who saw it would only further enrage the Americans. And questions were asked as to just how well German soldiers pressed unwillingly into service would actually fight, in a country filled with mostly happy German immigrants. For good reason some of these German mercenaries were sent to relieve British garrisons in relatively isolated Gibraltar and Minorca, so those British troops could be free to be sent to North America, as predictions of German desertions very much came true. About 58 percent of the German mercenaries came back home, about 17,313. The other 12,000 stayed. Not many were outright killed, perhaps a fair number died from disease, but the rest we can assume- and hope- went native.
[mere personal anecdote: a professor of mine worked at the University of Virginia library, while getting his doctorate. He was periodically handed people wanting to verify their ancestors had fought in the Revolution, in order to join the Daughters of the American Revolution. It was not what you call rewarding work, and he said that he took far too much delight in saying "sorry, dear: looks like you've got a Hessian".]
Lowell, E. J. (1884, reprinted 2010). The Hessians: And The Other German Auxiliaries Of Great Britain In The Revolutionary War. Kessinger Publishing, LLC.
Woelfel, M. (1948). Memoirs of a Hessian Conscript: J. G. Seume's Reluctant Voyage to America. The William and Mary Quarterly, 5(4), 553–570. https://doi.org/10.2307/1920640\