So much has already been written about what the Sox should do to fill out their roster before a season starts, whenever that occurs. 2B, RF, and SP are usually the top 3, with backup catcher and further BP depth also listed.
For my money, I believe that re-signing Carlos Rodon should be the Sox #1 priority, and if that was all they could do, I'd be okay with that. Here are the reasons.
1. Rodon finished 34th in baseball with 5 WAR last year. https://www.espn.com/mlb/war/leaders That was the second highest total on the team, behind Lance Lynn's 5.4 WAR. Tim Anderson was the only other Sox player ranked in the top 50, coming in tied for 47th at 4.6 WAR. (NOTE: I'm drawing WAR numbers from different lists that don't seem consistent, but I don't think if you plug in Baseball Reference or FanGraphs numbers that it changes any of these points.)
2. The Sox without Rodon have only 1 lefty starter - Dallas Keuchel - and he had the worst season of any Sox starter last year. He was so bad down the stretch that he was left off the playoff roster. The Sox badly need a lefty for some balance.
3. Even with the lockout, the Sox need to keep their starters fresh into October if they want to advance in the playoffs. The meltdown of their starters against Houston doomed the Sox chances. By adding a 6th starter, and one who can slot at the top of the rotation, the Sox should be able to ease the workload on all so they are pitching strong late. The last Sox team to win the WS in 2005 was led by a dominant starting staff. It may be old-school now, but that's partly because no team has a dominant starting staff. By bringing Rodon back and easing in Kopech, the Sox could have the best starting staff in baseball.
4. A corollary of #3 is that the Sox have at least 2 starters who need innings limits -- Michael Kopech, because he's not fully up to speed yet, and Dallas Keuchel, to keep him from vesting his option. If the Sox don't add a starter like Rodon, they'll be forced to dip into far inferior starting options to cover for those limitations. And this doesn't even factor in potential injuries that inevitably occur.
5. The Sox are not going to come close to signing a similarly impactful player for 2B or RF. Here's a list of free agents by position, with WAR listed, and including those signed. https://www.mlb.com/news/mlb-2021-22-free-agents-by-position At 2B, the White Sox actually already signed the 3rd highest FA by WAR in Leury Garcia, at 2.4. To get a higher WAR FA 2B, the Sox would have to sign Trevor Story and move him to 2B. That's just not going to happen. For RF, everyone's favorite is Michael Conforto, listed on that chart with a 2.9 WAR. (Not sure where that WAR number comes from, as Baseball Reference and Fangraphs both have him at 0.8 WAR in 2021 and only 2.1 WAR in 2020). That's not much of an upgrade from the trio of Sox players eligible to fill out DH/RF this year -- Sheets/Vaughn/Engel.
6. Rodon is going to be way more valuable as a TOR ACE than the 9th player in the batting order at 2B, or another bottom of the batting order hitter in RF. The Sox have Anderson, Moncada, Robert, Abreu, Grandal, and Jimenez penciled in from 1-6. They aren't going to add anyone who will supplant those top-6 batters. Meanwhile Rodon was the best pitcher in the AL in the first half last season.
7. Rodon doesn't hurt or slow the development of anyone on the Sox -- he essentially just hastens the elimination of Dallas Keuchel, who needs to be phased out anyway, and when gone his salary will cover most of the cost of Rodon's contract. But if the Sox add a new RF like Conforto, not only will that stunt the playing time of Andrew Vaughn, Gavin Sheets, and Adam Engel, but if he's signed for multiple years, it may slow the arrival of Oscar Colas and/or Yoenis Cespedes, at least one of whom should be the Sox RF within a couple years. Meanwhile, at 2B, the Sox also have multiple guys who are in development, including Romy Gonzalez, who hit 24 HRs between AA-AAA last year, and Yolbert Sanchez. Granted, they may not be ready to contribute in 2022, but the Sox still have Leury and should be able to add a cheap stop-gap player. For the Sox to pry away a better 2B, they will have to make a trade, which means weakening another position (or 2) to strengthen 2B.
8. Even though my argument is to sign Rodon #1, that wouldn't by itself preclude the Sox from improving at 2B or RF if they found the right fit.
Will the Sox re-sign Rodon? I still think it's possible. I think they didn't offer to tender him because I think if they sign him, they hope to get him for somewhat less than that number, given his late-season arm fatigue and prior injury history. I believe the Sox are hoping no one gives him a big multi-year contract, and the Sox will be able to match whatever offer Rodon can get on the open market. I also believe that if the Sox are ready to match what any other team offers, that Rodon would choose to return to the Sox, because he likes the team and his pitching coach in Ethan Katz, who began to unlock his potential.
As for the money, the Sox could cover most of the cost by trading Kimbrel. But I actually think the Sox are going to keep Kimbrel and go for it in 2022, hoping that he bounces back and gives the Sox a killer bullpen to go with dominant starters.
Pitching, if you have it, should win in the postseason, and the Sox pitching has the potential to be even better than their dangerous offense. Carlos Rodon would be a key part of that.