1 - Does such direct promotion actually work? My vague impression is "poorly, at best".
2 - How much overhead cost (especially legal & bureaucratic) does the promotion create? Note that politicians getting to congratulate themselves on being yet more pro-marriage is not a benefit for society.
Prior to like, 2017, the tax code used to impose a significant marriage penalty on couples with similar incomes; now it only imposes some smaller penalties. It is extremely recent that the tax code wasn't an active disincentive to get married for many couples. Being married is mostly not rewarded, unless one partner is a homemaker.
(Home ownership, parenting, and charity are rewarded by the tax code in a way that is unrelated to marriage.)
2 - How much overhead cost (especially legal & bureaucratic) does the promotion create? Note that politicians getting to congratulate themselves on being yet more pro-marriage is not a benefit for society.