The first issue here is that the NPS treats people like an annoyance to their job of walking around pieces of stone all day.My Daughter is a Park Ranger at the National Mall (to include the World War II Memorial), and I'm sure she'll be thrilled to learn that all she does is walk around pieces of stone all day. Rangers provide interpretation, answer questions, give directions, provide security, and generally enhance the visitor's experience. And they do it for very little pay.
Let's sit back for a moment and consider that putting your feet in the WWII pool is not disrespecting anyone.This was the architect's intent, and the Rangers will not prohibit you from doing so. They WILL, however, protect the overall solemnity of the Memorial. That means you can dip your feet on a hot day, but you may NOT use it as the neighborhood splash pool.
Our remaining World War II veterans frequently visit the Memorial, via Honor Flights or on their own. They'd like to be able to take it all in without listening to a bunch of people frolic in the fountain. And I, for one, respect the phenomenal sacrifice they made, the one that ultimately allows you to decide what's respectful for all of us and allows you to disrespect the Rangers that are there to protect and enhance the Memorial.