I am one for punting saves. My perspective is this: If one team has (for example) 4 relievers and I have 4 starters, on average my 4 starters will get more opportunities for wins and strikeouts than 4 relievers (which would contribute to Saves). So that's 2 categories to 1. WHIP and ERA are mostly affected by starters even if you have 4 relievers since it's unlikely that relievers will pitch enough to affect your weekly ERA and WHIP numbers (e.g. 20 IP for 4 relievers would be a lot, which equals about 3-4 starters starting once).
I have won once and placed in the top 3 two other times with one or less closers on my team (yes - thanks to good starters and a solid offense). I replaced the closers with very good set-up men who would occasionally get wins, and would also put up in the 100-120 K range.
HOWEVER... that was out of necessity. The closers in my auction went for quite a bit (even the #20-30 closers were going for $10 on a $200 cap). I basically couldn't afford them. If I HAD 2 closers, that's enough to compete in that category. Last year I only had Jose Mesa, and he was enough to win the saves category for me a few times.
Punting saves is a viable strategy, but I would do it out of necessity and would not move closers you have already. Plus you can always look to pick up the "out of nowhere" closers that come every year, giving you 3 closers which is very solid in a 12 team league.