Well, I don't think that one can really argue that the single club argument "went out the window" when Kane (eventually, finally, belatedly) left Spurs.
After all, he had already spent the vast majority of his career with Spurs - and is one of the closest to the "single club for most of his career" style players in the current game (still) playing at an elite level (for this is something that - I suspect - may be a lot more prevalent in the lower divisions); departing for Bayern - after well over decade with Spurs - in the hope of winning a trophy doesn't negate the argument that Kane clearly values loyalty and longevity.
Yes, I know that the current game prizes success (and the sort of greed that leads to trophies, recognition, and success), and a sort of brutalist expression of ambition on the part of players (and yes, I am perfectly aware that the duration of a player's football career tends to be quite short), but I have always thought it rather depressing that relegated clubs are so thoroughly ransacked of playing talent that it resembles a crude fire-sale, while the subsequently assembled relegated team often bears so little in common with its immediate predecessor that it can hardly be recognised other than the fact the players wear the team kit, while other, well run clubs, (Southampton used to be one such) can only (barely) survive by selling on talent that they have carefully nurtured, and are little more than nurseries, rather than teams that can realistically challenge for a trophy.