There are at least two ways in which to look at this question.
We can ask if it was a reasonable policy in terms of the United States’ ability to back it up at the time that it was issued. If we look at it like that, it was not a reasonable policy. The reason for this is that the US was not a very strong country at that time. If a truly strong European country (England, for example) had wanted to colonize a Latin American country in 1820, there was no way that the United States was going to be able to stop them. Issuing a policy that you cannot enforce does not seem reasonable.
A second way to look at this question is to ask if it was reasonable for the United States to want to keep European countries from colonizing independent countries in the Western Hemisphere. Most people would say that this was a reasonable goal for the US. The US had been founded on the idea that countries should be able to break away from colonial masters and rule themselves. It was reasonable for the US to want other countries in its region to be able to do the same.
Therefore, this policy can be seen as reasonable or unreasonable, depending on how you look at it.