Are we stumbling into a new Cold War between the US and PRC?

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A lot of people worry about Russia, but it's clear that they are largely a threat to their proximate countries and little else. China, however, is another matter - they have actual real influence around the world, have provided an economic model for the authoritarians of the world and are providing a lot of capital for promised growth and the sort of prestige projects most developing nation leaders really want. Increasingly the US-China rivalry has shown up in the background of all sorts of political battles around the world, from obvious cases like the recent elections in Malaysia and the Maldives, to the internal politics of the Conservative Party of the UK.

It's pretty clear the US is also joining in. This includes under Obama, who attempted to economically isolate China with the TPP, but has doubled down under Trump. The strong tariffs on Chinese goods (presented under flimsy pretences of protecting American workers) are a clear indication that the interests that back Trump wish to sever economic ties with China, making conflict between the two nations less economically damaging.

The question is, do the citizens of China, the US and their respective allied states really want such a conflict?