It's a dumb system and the players almost always win anyway, unless they get spectacularly poor advice, so there's not much in it for the team except the possibility that that player will have his feelings hurt and hold a grudge somewhere down the line.
The Phillies sidestep arbitration whenever possible, which they also did on Tuesday with utility man Wilson Valdez, although with much less at stake. Outfielder Hunter Pence and the Phillies did not arrive at a new contract, so both sides did exchange proposed one-year salaries. The two sides can still reach an agreement before the February arbitration hearing, but this doesn't seem as scary a prospect either way because: (a) Pence went through arbitration with the Astros a year ago and knows the drill, and (b) he's about as sensitive as a ballpeen hammer.
Hamels has to be, and should be, handled a little differently. The biggest reason is that Hamels, more than any player on the roster, represents the best chance of quality future production for many seasons to come. If there is a Phillies player you are more certain will still be performing at an elite level in five or more years, please point him out. Time's up. There's isn't one.
The question isn't whether the Phils want to sign Hamels to a long-term contract, or whether Hamels wants that himself. Both sides want the same thing. They just have to figure out the small matter of the exact length and terms of the contract.
At the moment, Roy Halladay is entering the second year of a four-year contract (if he achieves very reachable vesting options for the fourth year) that pays him an average of $20 million per season. Cliff Lee is entering the second year of a five-year contract that pays him an average of $24 million per season.