I also worked at McKinsey. 5 years, with some of that time in the Johannesburg office. Agree with the above and don't have much to add. But AMA.
Will the big3 be around in 15-20 years or is it a dying industry with many of the best people leaving for exist opps in tech/finance/etc.
In my opinion, there will always be a need for large companies to bring in outside help to get very specific things done (largely due to their size and dysfunction). MBB are smart enough to generally move where help is wanted. Just in my time there I saw them hugely lean in to big data, design, cloud, AI etc. And when they invest they go big.
That being said I personally would never bring in MBB for a purely technical implementation project. Way too expensive and the value is not there right now.