The John Gray book about dating (something like Mars and Venus on a date) goes into depth why it is so important to let the man pursue--he will be turned off by a woman taking this role, as the "fun" is in the pursuit. The more he has to work at it through the first 3 stages (ultimately there are 5), the more you'll set yourself up for a good, committed R in the future.
Many guys never get do get there, because they are such a "catch" that women throw themselves at him and he gets complacent and lazy. I'm sure this is the dynamic I set up for myself in my marriage as I pursued my H in stage 3 (still important NOT to purue in this stage either!) Men need the "workout" of pursuit in order to build up the "muscles" and do the work it takes in the R.