My older son ( HA D3) had "offers" and asked to commit ED and EA depending on school. not every school had ED. No coach made mention of $. It was all about just getting in. $ was at the discretion of financial aid office and admissions. those decisions came out in the spring. He went EA and RD so he would know what we had and could afford. Some schools supported him some did not and supported others. Also if a coach at D3 can help with admissions, it may be only for a few slots. Many HA D3. schools coaches have 0 influence on admisdions. coaches do ask for commitments because they are trying to put together rosters and fill needs so they want to have an idea of who is coming.
FWIW my son applied RD to his school got notified early of a good merit scholly should he accept and was asked by admissions to visit along with others of same as a recruiting by admissions. He he did "commit" until the last day of april