The flaw in that line of reasoning is assuming that luck and connections are the opposite of skill and execution.
Building relationships is a core part of business development, if a business lacks appropriate connections then it's something they should work on either by building bizdev skills internally or hiring. In the same way that if someones a tech founder with no marketing skills, they have to learn it or hire for it. You're not going to win just by having the best technical product, you have to have the best business.
Similarly luck isn't automatic, if you work to put yourself in positions where you have the opportunity to be lucky you're much more likely to have that luck. One of the big advantages of being in startup hub like SF is you're moving somewhere where your far more likely to have valuable serendipitous meetings than anywhere else.
The number of people whose "luck and connections" come from "skill and execution" is smaller than the number whose "luck and connections" come by accident of birth. This is true no matter where one lives, or how one wants to leverage his own skills.
While it probably varies between different fields, I haven't seen any evidence for that in the startup world.
There's obviously a certain level of "accident of birth", you have a much better chance if you were born in a developed country, one where you can go to university, etc. But if we standardise at say pool of CS graduates from good universities it's certainly a much more level playing field.
If we take what's probably the most important relationship in the startup world, that of co-founders, most co-founders meet each other through work, actively seeking through professional networks or university. There's very few co-founders who met through family connections.
Similarly for investors, investors will take a recommendation from one of their portfolio founders who've worked with someone much more seriously than that from a family friend who just knows someone socially.
One does have a much better chance if one is born in a developed country--but it's still a small chance.
Also, a "pool of CS graduates from good universities" is already biased toward people who were born into (relative) privilege. Have you considered that you "haven't seen any evidence" because you are effectively excluding from your analysis a large quantity of the data?
Look, I'm not saying it's pointless for those who were born into poor or middle class (or even many upper-middle class) families without connections to try. I'm saying it's disingenuous to pretend that a system that self-selects against those very people is somehow a meritocracy or that it is not, in fact, self-selecting against people who aren't, essentially "born lucky."
Building relationships is a core part of business development, if a business lacks appropriate connections then it's something they should work on either by building bizdev skills internally or hiring. In the same way that if someones a tech founder with no marketing skills, they have to learn it or hire for it. You're not going to win just by having the best technical product, you have to have the best business.
Similarly luck isn't automatic, if you work to put yourself in positions where you have the opportunity to be lucky you're much more likely to have that luck. One of the big advantages of being in startup hub like SF is you're moving somewhere where your far more likely to have valuable serendipitous meetings than anywhere else.