From an American perspective, we can cut individual trade deals with whoever we want, because every country wants access to the American consumer. That is why we have a giant ass state department. We don't need giant TPP deals filled with a wall street christmas list of horseshit.
The reason we might have large, group, trade deals with "a wall street christmas list of horseshit" is because tariff's are actually relatively low in many places, and in any case, tariff's are far from the only, or even biggest, thing that might be a roadblock to trade.
Really, these deals are much more about stuff like countries unifying regulations (maybe having 1 set of automotive regulations to comply with instead of a whole bunch, for example), strengthening intellectual property in countries where it is weak, and (ideally) setting minimum standards across a large, and thus influential, block of countries to curb a race to the bottom (and the TPP would have raised environmental and labour standards in a number of countries).
These sorts of things have been attacked as not actually having anything to do with trade, but they really do. IP stuff specifically gets attacked a lot, but creative industries are a big part of the American economy, and they employ a lot of people. You'd think people wouldn't be so aghast at the idea that IP rights would be considered an important part of trade between countries.
This does leave us negotiating a lot of policy between countries, usually in secret, which is very unpopular. But agreements that merely reduce tariff's wouldn't really achieve much. And I get that maybe some of the provisions might be flawed. But my argument isn't just that free trade is good, but that there are good reasons the TPP would touch on so many topics that many wouldn't think would be part of a trade deal. (The full text of the deal is publicly available, so people can be specific with their concerns if they'd like)
And when people talk about the TPP holding China to higher standard this is what they're talking about. If enough people signed on to the TPP the other countries in the region will be pressured to then also sign on, accepting the unified regulations and minimum standards that might become the rules driving trade in the region.