the precursor of baseball was British, but it was not Cricket...it was Rounders.
Right, as I said, the precursor was British. I wasn't suggesting it was Cricket, sorry if I gave that impression.
Baseball is sort of a combination of the two, with some American ideas thrown in there.
There are two main reasons why baseball overtook cricket in the USA.
(1) Americans want to be in charge, and they couldn't be in charge of cricket. So they poured their money into baseball (a game Americans invented and therefore could be in charge of) and developed the professional game, while cricket in America remained pretty much amateur.
(2) England shut us out of international play in the early 20th century, by forming the "world" governing body of cricket, the Imperial Cricket Council. Only England and its colonies could be members. This was mostly done because they've always had it in for us because we fought for our independence.
Prior to this, though, some English teams did tour the United States and some US teams did tour England. Australia did tour the US up through the 1930s. Don Bradman in fact visited the USA and met Babe Ruth at a match in New York City, a story which I am trying to do some more research on.
Now the Imperial Cricket Council has renamed itself the International Cricket Council and has opened itself up to all nations. The United States has also been flooded by immigrants from India, Pakistan, and the West Indies (and some from England and Australia), who play the sport. The ICC is now looking to try to tap the US market, meaning, non-immigrants like most of us.