When there are other big differentiators, and the CS issue in question is not serious, then yes, the non-CS factors are likely to dominate decisions.
But often this is not the case. I find that while good CS can make customers happy in normal circumstances, CS really makes or breaks a customer relationship when something goes wrong. Good CS and you have a brand advocate. Bad CS and you may have a nemesis that will go to irrational lengths to tarnish your brand out of pure spite.
I left my old cable operator for two reasons: 1) they were unable to fix my cable internet for two weeks, 2) their customer service kept giving me the wrong information.
Of those two, the latter was by far the most important factor. The former was just the trigger that put me at the mercy of their abysmal CS processes. Before that, if you'd asked me, I'd have recommended the company, and been totally neutral about their customer service, as I'd not had to deal with them for anything of substance.
Leaving did not get me internet back faster. It did not get me better service - just different. But it gave me the satisfaction of telling them to f-off, very publicly, after I'd suffered through multiple days of regular calls to their customer service team.
The downtime made me annoyed to start with, but their CS team who could have defused the situation just with some basic courtesy - others have - massively escalated things by being unsympathetic, not passing on the right information, not calling back when there were changes to the situation, and the final straw: after I'd decided to cancel, and had waited in line 45 minutes, I was told the computer systems were down and when I asked if they could take my details and arrange it later, they said no - ok, but could they call me back? No. I was expected to call back, wait in the same queue again for who knows how long, without knowing if they'd manage to cancel for me then.
So just by attitude and a few process issues that would not have made a material difference to their cost, first they lost me as a customer, then they pushed me into publishing a scathing complaint on my blog and tweet about it. I "only" have a direct reach of a few hundred people, but apparently that worried them enough that I had a call from someone claiming to be an assistant to the CEO the following (Saturday) morning, asking how he could help.
While that calmed me somewhat, had they just had better processes in place, they'd have had several thousands pounds in additional revenue from me by now, and not wasted a dozen or so CS reps time with all the repeated calls that arose from their poor internal communications.
That's why good CS matters.
It's those cases where long term previously satisfied customers decides to blacklist you for life and starts to badmouth you to every friend, co-worker and relative just because your CS processes made them angry by unnecessarily escalating some minor problem.