"Monroe Doctrine" is ultimately a fancy way of saying sphere of interest. Unless you create a US without any foreign interests, but rather walled themselves off, they're going to have a foreign policy which looked after their business interests. The US wants a North/South/Central America which is open for US business, not closed off by an European overlord.
Regardless, for the first ~ 100 years of the Monroe Doctrine, the US had no means to enforce it, and the Europeans did not recognize it. During the Venezualan Crisis of mid 1890's, the US pushed the MD to a whole new level, and Britain was busy with other world issues, so they backed down and recognized it.
Ultimately, though, Britain was Boss (sphere of interest) in Canada, in South America, and a lot of central America, only ultimately losing out in WW1/2. With the exception of a few central american countries, the US was not instrumental in the formation/maintaining latin countries/gov'ts. When they did, it was because of business interests, not explicitly because of a declaration of a MD. Then came the cold war, and that whole struggle had nothing to do with the MD, except in a generic way.
declaration of MD or not, everything remains pretty much exactly the same, unless you turn the US into a closed, inward looking, business society.