Actually, the goal was to eliminate a lot of that.
In trade, countries usually have two general aims:
1. Negotiate reduction or elimination of tariffs in foreign markets so that domestic producers can expand abroad.
2. Protect their own domestic producers from foreign competition by retaining the import tariffs that keep them competitive.
So, Japan subsidizes its domestic rice farms and tarrifs rice imports, but wants to sell its cars unfettered. Brazil wants to export its oranges and other produce more, the US wishes to export more of it's beef and cattle market. (These are the ones I'm thinking of off hand.)
The thinking goes however, that nations will gain more if they can all agree to open their tariffs, and allow goods to "trade freely". This means that while there will be short term disruption and decline in some markets, that their economies will have net growth on the whole, because economics is not a zero-sum game. For the TPP, the math is somewhat easy: One or more domestic industries will face internal competition, while their export markets will now be open to a dozen new countries. If they all do this, it's a net gain. (So the thinking goes.)
The portions that people seem to take issue with mostly in our line of interest have to do with the intellectual property provisions. This is to shore up the mismatch in legal protections that exist in countries with weaker IP laws. You can more or less sum this up with pointing out that pirated software and media is sold openly in countries like China and Vietnam. The provisions pertaining to those are other countries saying "Look, we'll trade, but only if you respect our IP."
Whether or not you agree with those provisions is of course, the million dollar question, and on things like that, the fate of the TPP depends. But that's the rationale.
And yes, you're exactly right, a rising global standard of living is /exactly/ what everyone wants. It's not some evil conspiracy, it really is that. And so long as no one can game the system (too badly), that's exactly what will happen.
(More reading on that last point. Can't recommend it enough:
In Defense of Globalization - Jagdish Bhagwati
Fresh book recommendations delivered straight to your inbox every Thursday.