I had no idea this was an issue anywhere. I am guessing that in some states where the water is needed for streams, lakes or whatever, there could be an issue if a huge number of people collected water and thus prevented the natural run off. But my impression of NH - probably in error - is that you would have sufficient rain.
Here in California I collect rain water and use it to water trees, flowers, whatever. But I have not checked to see if there are restrictions on the collection - and most of our rain water ends up in the oceans as the politicians will not provide permits for dams to be built to store that water. So, if I don't collect the rain water I suppose that it - or its equivalent, goes into the ocean at some point,
The only other reason I can see is that if you collect the water and do not use it soon, it could be a place for mosquitos to breed.
Seems dumb and short sighted to me.