While agree with your theory on avoiding super large and long deals, one can make a firm case that just about every ring we have since 2004 was, at worst, aided by the signing of a long term FA, and at best, seeing the long term signing as an essential aspect of winning the ring.
On that "other site," I started one of the most responded to posts in history called, "No Manny- No Rings." (Later, I stared threads called "No Papi- No Rings" and "No VTek- No Rings," too). Without Manny's deal, IMO, we don't win in 2004 or 2007.
One can argue Papi's 4 year extension in 2005 does not qualify as a long term deal, but clearly he helped us win in 2004, 2007 & 2013. The same could be said of Beckett's 4 year deal in 2010 and our 2013 ring.
JD Drew's 2007 contract for 5 years can be debated and was for years.
John Lackey's 5 year deal in 2009 certainly was a key component in the 2013 season.
David Price's long term deal seemed essential to our 2018 ring.
Yes, the list of bad and mediocre long term signings by the Sox is long- perhaps longer than the good list, but long term deals have played an essential role in all of our championships.
Moncada's large signing bonus and tax netted us Chris freakin' Sale.
Castillo was a total waste.
CC & Pablito's deals, too.
Dice-K gave us 2-3 decent to very good seasons.
AGon helped us dump CC & Beckett and paved the way to the 2013 championship by allowing us to sign Vic, Napoli, Drew, Gomes & Dempster.
Pedey's extension was not needed for the 2013 ring season, and he was not an essential part of the 2018 season, but that deal was not a total dissaster.