Have US Income and Wealth Inequality Actually Increased?

You make my point: it is nonsensical to argue about "poor" when wildly contradictory definitions are being used. A great many legally "poor" in the USA have homes, cars, running hot/cold clean water, HVAC, cable TV, smartphones, etc. and a livable income plus generous free food. For other areas, having a little more than an objectively minimal nutritional intake, survivable shelter, adequate clothing, and mundane healthcare counts one as "not poor" despite still being well below the official US standard.

We need an objective definition of "poor" better than "can't get by on $X in the world's most expensive cities".

I create wealth by pure thought. Sure that sounds stupid to some, but it's quite true: with about a thousand dollars' worth of borrowed equipment, I sit here writing software to do things useful to my employer. I am not "extracting wealth", I am creating it, organizing electron flows to do things useful to clients, things they are willing to pay for whereby both of us (client & developer) benefit. It is my right to write software, my client's right to use that software, and our right to work out an exchange of representations of wealth. The only "extraction" happens by contracting the exchange of one thing/service for another, facilitated by the abstraction of currency; this creates more wealth in the system, leaving both in a better place than they would be otherwise.

My country's government was created to facilitate the exercise of rights by delegating limited powers to government. Insofar as the "shared system" goes, taxation exists to fund those limited powers, and arguably provide a minimal safety net to the truly destitute (insofar as charity is unable to). Beyond that, ownership is a respected & protected right, and the economy functions by people creating things to own (wealth) and exchanging representations of that wealth (money).

What you & other "wealth inequality" agitators "ask" for is theft, insofar as it demands - under threat of violence by those unrelated to that wealth - those who create or negotiate more wealth than others must, with no objective basis in ownership & contract, give to those who have done nothing for it.

I understand what we have is not a perfect system; that imperfection is a consequence of what some deem "original sin" (adjust terminology as your values see fit to match the point). Bad as it may be, it is better than any other system wherein one group extorts wealth from others without agreement or moral right thereto. Just because one manages to leverage opportunity better than others does not mean those others can "rectify" the situation by saying "we outnumber you, we've decided what you own belongs to us, and if you don't hand it over we'll do horrible things to you."

Yes, progressive taxation is institutionalized theft. Taxation should fund the costs of government carrying out limited powers to facilitate rights as delegated by the national constitution; insofar as income taxation is the current method, it should be blind (as justice should be). The counterpart to your notion that the wealthy exploit the system, is that the wealth pump the system too: their wealth is not squirreled away out of reach of the shared economy, it is rammed right back in thru investments, creation of markets for luxury goods, and prolific charity; the evil you impute is at minimum balanced by the good it creates. Every dollar should be taxed equally, as (on the whole) those who acquire more income do much in the shared economy with it. Insofar as sheer poverty fits in, I'll acquiesce to deducting a minimum income; if you're better off than objectively poor, you can do your fair share too.

Those agitating about "wealth inequality" always fail to objectively address the charity which the rich give to. Just because someone isn't giving money via taxation doesn't mean they're not doing tremendous good; confiscating more by taxation reduces what they can and do give by other ways.

And, just to hammer the point home yet another way (however palatable it may or not be): in a well-armed population, "majority rules" is not sufficient grounds for confiscation. There are a LOT of people prepared to fight back against the self-appointed redistributors of wealth. They know the consequences, so don't want to go there, but will if it comes to that.

TL;DR:

It's.

Not.

Yours.

We already give an enormous amount to the "poor". If you make less than a given amount, various welfare programs will fill the gap (some pushing you WAY above the line). It's enough that another problem is arising: many on welfare receive so much that they can't afford to work, lest they lose all those benefits and reap less net income as a consequence.

Again, I come back to the issue of defining the word "poor". As is, it's not objective relative to the recipient's survival.