We're not living in the year 2003.
Gary Sheffield is not a great player in his current form, nor is he better than Pat Burrell. You don't even have to know what wOBA means to understand this. Over the last three years, Sheffield's line is .254/.355/.436* with 50 homeruns. Burrell's line is .254/.385/.504 with 92 homeruns. Those are not comparable. That's almost .100 OPS points; the difference between Carlos Pena and Randy Winn is less than that, and Randy Winn is a good defender. Park-adjusted and in advanced terms, Sheffield has been worth about 21 runs these last three years. Burrell is closer to 70. One of these players is 40-years-old, that player just so happens to be a poorer offensive player.
Gabe Kapler and Gabe Gross are average players. Which to most means they're completely useless** but when you talk about non-DH positions, defense actually matters, and Kapler/Gross are good at defense, Sheffield is horrible. Before being shooed to DHing full time, he recorded UZRs that would make Burrell blush. I'm confident when I say Sheffield would be a -15 < x < -10 runs outfielder.
CHONE projects Sheffield at 4.5 offensive runs while ZiPS says 2.3. Let's say he's worth 5-10 runs offensively. Best case: he's a -10 fielder, 10 hitter, gets 600 PA, and plays RF everyday. That makes him worth 1.25 wins. Gross was worth 2.5 last year and Kapler 1.7. CHONE and ZiPs say about 0 for Gabe Kapler and ~2.5ish for Gross. Gross/Kapler are 0 < x < 5 fielders in the corners. So eight runs worse offensively -- if Sheffield finds a way to overcome his age -- and 10-15 runs better defensively.
Throw in Sheffield's ego and unwillingness to do what his teams so desire of him compared to the Gabes, and there's simply no reason to pull the trigger.
We're less than a week from the 2009 season, start acting like it.
*Fun with new B-Ref, 06-08 lines:
Yes, Gross only faces righties, but some people are calling Sheffield's bat "menacing". It's an insult to factual evidence, really.
**Until one hits a homerun and people swoon over how they exemplify the great role player winning teams need.