> Obviously it comes from the company; otherwise it's just a regular stock sale that doesn't need any additional descriptor.
This is incorrect. A buyback is when a company buys its stock. It is giving cash to shareholders, and taking the shares back. A stock sale is the opposite, when the company sells its stock and receives money from the new shareholders. The direction of cash flow is very important here, because a key difference between a Ponzi scheme and a buyback is that in a buyback, the company is distributing cash to investors, not taking cash in.
> The issue to me is that the division between "money companies get from selling their shares" and "money companies get from selling their products" is artificial
If you're collapsing these two, you're generalizing beyond the point of usefulness, and ignoring all of the reasons why people engage in economic activity in the first place.
There are many, many industries where the consumer does not even get to sell the object again in the future. When you go out to a restaurant, the meal disappears within an hour, leaving you with just memories and indigestion. When you go to an amusement park, you have fun while you're there and leave with nothing. When you pay rent, you have a roof over your head for the month and then nothing afterwards. When you go to a casino, you get your hopes and excitement up while you're there and leave with less than nothing. When you buy alcohol or tobacco, you're spending money on the privilege of poisoning yourself.
Almost everyone would consider these legitimate economic exchanges, though. They may be inadvisable on a time-preference basis because your money disappears and you end up with nothing durable in return, but few people would argue that a large part of our economy is made up of transactions like this.
You're right though that you can take the corporation out of the equation and they still make just as much sense. If you take the corporation, its accounting statements, and the corporate treasury out of the equation, then a buyback is taking money earned from providing goods and services, and distributing it to the shareholders. The difference from a dividend is which shareholders receive the distribution: in a dividend it is distributed equally across all shareholders (who continue to remain shareholders), while in a buyback it distributes the cash to the people who least want to own the business in the future, paying them out entirely and distributing future profits to a smaller set of shareholders.
When a company buys stock, the money comes from the company. You're literally saying the same thing as me and telling me I'm wrong. It's not worth it for me to read beyond that because it's not clear you're reading what I'm saying properly.
The issue to me is that the division between "money companies get from selling their shares" and "money companies get from selling their products" is artificial; whether it gets taxed differently is a procedural issue, not something that inherently defines what "value" is. When the value of something is only from selling it again in the future, it's inherently only valuable as long as there's someone else to pass it onto to sell it again later. Sticking the company in the middle of passing it along doesn't magically change whether it's sensible or not. That's what I mean by "effectively a Ponzi scheme", even if it's not strictly one in the definitional sense. The same arguments for why a Ponzi scheme is undesirable apply.