Take two individuals with the aptitude and the willingness to learn engineering and pass said exam. Give one person enough money to pursue an engineering degree. Burden the other one with an ailing parent. There is no conflation here.

Similarly. Take two people with the aptitude. Have them both spend a year messing about. One of them has a family who can afford to help them get back on track, the other doesn't.

I'm doing really well despite falling off the rails a bit in my early 20s. If I didn't have my family to help me, I'd not be doing nearly as well.

That's not my point. My point is that the 'geometric increase' for real competence or aptitude is not the same as the compounding 'merit' of a billionaire which may well just be some monotonic increase in the value of some company within which they have a stake. Your issue is a different one, and yes, if both of them are 'good enough' perhaps they should go through a random selection process.

Of course there are different things.

But what is merit? Take the "aptitude and the willingness" in the other reply: we cannot decide to be naturally driven or passionate about something, or being quick learners and so on.

We can only decide to put efforts into something. Unless our energy is depleted by issues that we cannot control, ranging from being concerned about financial difficulties, family issues, to physical and mental health, and so on.

Meritocracy really means eliminating the issues that can be eliminated.

And that's much harder than it sounds because so much of this culture is based on maintaining and perpetuating privilege.

To be clear - the US caste system is ridiculously rigid and self-sustaining. It has no interest at all in being more permeable to social mobility.