I think you misunderstood much of what tomp said, and willfully misinterpreted some of the rest.
The number of trades does not determine alpha, but it means that you can be much more certain about whether someone has alpha or not. For example, John Paulson made billions on (essentially) a single trade in 2007 and early 2008. Does he have alpha? It's hard to say, because all of those profits were from one trade, and he could have been lucky. Virtu Financial generates millions of dollars each year, by making tens of millions of trades. Do they have alpha? Absolutely - you can be certain of it, because it would be statistically impossible to get lucky tens of millions of times.
The idea "alpha becoming beta" is an extremely relevant one for many hedge funds today. As strategies become well known, they become commodified, and are often offered at a lower fee, both by hedge funds, ETFs and investment bank products. Frequently, they are offered for little or no performance fee, so they cannot be called "alpha" and are often referred to as "smart beta". For example, AQR Capital Management offers many low-fee funds giving exposure to value investing, momentum investing, managed futures, the FX carry trade and others. It sounds like you are using a very narrow definition of beta (exposure to the stock market) whereas the usage in the industry is much broader.
Pointing out that quant funds use "algorithms" to trade rather than "computers" is pointlessly picking holes. It's clear what he means.
The number of trades does not determine alpha, but it means that you can be much more certain about whether someone has alpha or not. For example, John Paulson made billions on (essentially) a single trade in 2007 and early 2008. Does he have alpha? It's hard to say, because all of those profits were from one trade, and he could have been lucky. Virtu Financial generates millions of dollars each year, by making tens of millions of trades. Do they have alpha? Absolutely - you can be certain of it, because it would be statistically impossible to get lucky tens of millions of times.
The idea "alpha becoming beta" is an extremely relevant one for many hedge funds today. As strategies become well known, they become commodified, and are often offered at a lower fee, both by hedge funds, ETFs and investment bank products. Frequently, they are offered for little or no performance fee, so they cannot be called "alpha" and are often referred to as "smart beta". For example, AQR Capital Management offers many low-fee funds giving exposure to value investing, momentum investing, managed futures, the FX carry trade and others. It sounds like you are using a very narrow definition of beta (exposure to the stock market) whereas the usage in the industry is much broader.
Pointing out that quant funds use "algorithms" to trade rather than "computers" is pointlessly picking holes. It's clear what he means.