Fourteen of the top potential free agents received a qualifying offer this year, including our own Eduardo Rodriguez, and big names like 2B Marcus Semien, SS Carlos Correa, OF Nick Castellanos, RP Raisel Iglesias, SP Robbie Ray, etc. Any of those fourteen players would help upgrade the Red Sox roster, but there is a catch: besides Eduardo Rodriguez, if the Red Sox were to sign any of those free agents (assuming they reject their QO and officially become free agents) they would forfeit their second highest pick in the 2022 MLB draft.
Most years this would entail a late second round pick for the Red Sox. However, in 2020 the Red Sox stunk and were rewarded for their failure with the fourth overall pick in the 2021 MLB draft. In the second round the Red Sox selected Judd Fabian with the 40th overall pick. Judd Fabian did not sign with the Red Sox. As a result the Red Sox now receive the 41st overall pick in the 2022 draft as compensation. This is in addition to having the 24th overall pick in the draft as a result of what place they finished in this year. So, unless I am mistaken (I am hoping one of the rules gurus fact checks me on this), if the Red Sox were to sign a player who received a QO they would lose the 41st overall pick instead of a later second round pick.
Is this significant? Those intimately familiar with the MLB draft know that it's not just about where you pick but also about how much bonus pool money you have to try to entice players to sign rather than going to play in college (or returning to college). Based on last year's numbers the 41st pick carries a slot bonus of about $1.8 million. By comparison, their first and second round picks carry values of approximately $2.8 and $1.2 million respectively. In short, Judd Fabian not signing last year means that signing a FA with a QO this year will sting 50% more than it otherwise would have.
I don't know that this will definitively take the Red Sox out of contention for any of those top free agents, but it is a factor that they will have to take into consideration if they hope to simultaneously contend and replenish the farm system. There are still some top FAs out there they could consider that for various reasons did not receive a QO.
Javier Baez, for example, was traded mid-season and so could not receive a qualifying offer. Usually a SS, he played 2B for the Mets last season and could help replace the offense we'll likely be losing with Kyle Schwarber (who also does not have a QO attached to him for the same reason).
At SP, Max Scherzer and Kevin Gausman have previously received QOs, so they were ineligible to receive QOs this offseason. The White Sox simply decided not to give Carlos Rodon a QO despite his stellar season.
Most of the RP FAs are unburdened (Raisel Iglesias being the lone exception), likely because those players are typically valued below the $18 million a QO entails. This is another area of need the Red Sox have and another place where they can spend money on guys like Ryan Tepera or Joe Kelly without losing a draft pick.
In short (too late), signing a FA who received a QO would be more expensive this year than in usual circumstances because the Red Sox actually have a pretty high second round pick. They could still say "screw it" and sign Marcus Semien, but there are a lot of other good options out there they could consider that don't involve losing that draft pick.