Thanks for joining us. The short answer is that the U.S. Constitution limits what government can do.
A purely economic explanation such as you've offered in your two bulleted points isn't politically sufficient to justify a law. Let me offer a more detailed response to illustrate, but please don't take it as criticism:
Contested point: It would increase the amount of tax going to social programs.
The US is a republic, where the U.S. Constitution limits the power of government. There's no mention of "social programs" in the Constitution, that is not one of the enumerated powers, so some U.S. citizens might well argue increasing taxes to achieve these ends is unconstitutional. But let's say that's a minority opinion, and that oh let's say 70% of Americans agree with you. Does that justify it based on "majority rule"?
The framers of the constitution recognized that they did not want majority rule. That sounds undemocratic, but in doing their historical research the founders discovered that democracy has its problems, and the biggest of these is fairness to minorities. To illustrate, let's say 70% of Americans were religious Puritans. Would we allow a law saying everyone should join a Puritan church?
Contested point: It prevents companies from growing excessively big.
Here too you're letting opinion enter into it. What says there should be a limit on how big companies are, or what measure of bigness should be used?
Again hypothetically, let's say that 70% of US citizens owned stock in Costco. Costco, while a for-profit company benefits the citizenry in general: Yes the 70% profit from their ownership of Costco, but under the principals of capitalism non-owners still benefit from Costco's putting downward pressure on prices across the consumer goods market. Capitalism holds that benefit exists even if it's only 1% who own Costco stock, as long as Costco doesn't hold and abuse a monopoly.
Now let's say I am one of that 1% minority owning Costco stock, but that I'm not rich, I just got it as a fringe benefit of being a Costco employee. Should my benefit from Costco's profits be taxed higher because Costco is successful? I think not, and I'd suggest that fairness is the strongest reason to oppose progressive taxes on corporations.
If on the other hand Mr. Doe was a rich Costco stock owner, the progressive tax on individual covers him without penalizing me.
P.S. Macro economics is explicitly on-topic here. Thanks for asking.