I agree with your sentiment, but I think the extreme of your tone might put some people off.
These buttons have bothered me for a long time because it just illustrates how short sited the thinking is in our government institutions.
This small lie may reduce jaywalking by 3%, in the short term.
But for the future generations growing up in a world where the government makes buttons that don't work, public trust will erode, conspiracy theories will seem more reasonable, and most importantly government employees will have a new standard to weigh their decisions against. If lying was permissible in this case for a slight benefit the maybe a slightly more egregious lie would be acceptable in a different situation.
And on a separate note, once you expect these buttons to be fake people stop pressing them. When you then encounter a "real" button you miss an entire cycle on the crosswalk because you have been trained to ignore the buttons, and this results in people getting absolutely furious.