Since we are speaking of false dichotomies anyhow, I think that the OBP/SLG one counts double, not just as the idea that a player only possesses power or on base skills, but also that playing around with them in a theoretical line-up efficiency tool has a very realistic relationship to run scoring. The thing that those tools do is very normalize expected outcomes in aggregate, which means making some assumptions about the sequencing of events in a hypothetical inning/game. In all the worry about walks vs XBH, what is lost is that the tools is making the assumption about the average distribution of the most common event included in OBP/SLG calculation, namely hits.
In real life, (the basis for our assumptions about the Red Sox needs vis a vis power/on base), the problem for the Red Sox hasn't really been a lack of power. To be sure, they have been middle of the pack (16th in the majors in SLG, 15th in ISO), but not terrible. The issue is trying to figure out why a team that is 3rd in the MLB in baserunners(!) and has hit for average power, is also in the middle of the pack in run scoring.
Looking at something simple like "run efficiency," which is just runs divided by baserunners (R/(H+BB+IBB+HBP)), we see that the Red Sox are the 4th worst in the majors, at 31.22% (the range of outcomes is from 28.75% - 42.08%). Normally, looking at the list, there is a strong correlation between base runners and runs scored, no surprise there, that's the principle that much of the OBP/wOBA concept is based on. Further, most of the teams at the top of the runs scored list combine lots of base runners and a decent run efficiency, which makes sense too. We can all agree that runs scored is a function of having opportunities (base runners) and capitalizing on them.
We know that the Sox have had tons of opportunities in terms of base runners, but what we see during the games as "failing in the clutch" is in fact not completely contrary to the factual matter that the team is great at not making outs, in that they often find ways to not make outs that don't score runs. Looking at the total baserunners, and then looking at the ratio of those base runners that come from actual hits, vs BB/HBP, reveals where the Sox are the real outlier. The average team gets 69.76% of its base runners from hits of some kind, regardless of the total bases/SLG value of that hit (since 1 TB for the batter can often advance the lead runner 2 bases).
The Red Sox are dead last in the majors at 61.96%.
We are second in the majors in walks and HBP, but 24th in H/PA. OBP is great for getting opportunities to score, which correlates well with runs given an average distribution of hits as a component of triple slash numbers. However, a team made up of guys who all have a .350 OBP AND hit .300 will score more runs than a team is all guys with a .350 OBP and a BA of .250, because those extra hits will convert more of the opportunities to runs than BB/HBP will in the same situations.
Not making outs is super important because scoring comes from opportunities, but we need good hitters, it's not just an argument of "good at not making outs" vs "good at hitting for power." Right now we have a team that is amazing at not making outs, but not great at hitting, and they aren't the same thing.