Sure, losing a key player due to FA, especially when you can't afford to re-sign said pick is rough. Trust me, as an A's fan, I had to deal with almost losing the entire outfield with David DeJesus and Josh Willingham leaving. Willingham might have been worth re-signing, but getting that pick in the sandwich round, in this case, drafting high school infielder Daniel Robertson might be a better long term plan for a team that's not currently contending.
Now for the A's, this method of signing FA and getting comp picks in return changes in the new CBA. If the player is in the final year of their contract, there is no comp pick involved.
Not always do these clubs get the short end of the stick, there's been quite the gems in the sandwich round.
By far David Wright has been the most successful sandwich round pick since 2000. Between 2001-2006, the Gio Gonzalez vs Justin Speler set and Joba Chamberlain vs Tom Gordon set were the only other notables worth mentioning. The Clay Buchholz vs Pedro Martinez set and Huston Street vs Miguel Tejada set were the only that favored the departing FA rather than draft pick.
The sandwich round picks after 2006 mentioned have yet to make a big league splash, but surely, the Travis D'Arnaud pick from losing David Delucci, Mike Olt from Ivan Rodriguez and Nick Castellanos from Brandon Lyon should favor the picks. All the prospects mentioned at the top of the graphic all represent the top of their team's farm systems according to Baseball America.
I'm excited to see how these players shape up in the coming years.