Which moral doctrines/strictures do you think it violates?

Basic fairness

It's a tradeoff. Suppose you are relegated to trading once per minute and you need to allocate $x per trade to make a profit. If you can trade 100 times per minute you need $x/100 to make a profit.

Or, maybe your strategy doesn't make money when you can trade once per minute, but does at a higher frequency.

What is fair about saying someone has to have 100x the capital to participate? You are focusing only on one dimension of cost, when there are several.