Initial impressions are driven by strength while lasting impressions are formed by your weaknesses. So building up those strengths will get you the job offer, but bolstering your weaknesses is what gets you the promotion.

I also heard that McKinsey adheres to that strategy when investing in training for their employees. Though that is only hearsay and it doesn't mean anything, they could also be wrong. But I think you are right when saying that the opposite approach also has a lot of followers right now.

I suspect what's best for an employer isn't necessarily the same as for an employee. Big employers want specialisation and obedience. That's fine while the demand is there but the narrower your specialisation the less the market needs to move to make you obsolete.