Wouldn't this have the perverse incentive of poor people wanting large emitters to keep emitting, because it directly puts food on their table?

In a sense yes, but I wouldn't call that an incentive, any more than I have an "incentive" for Chipotle to give me free burritos. I'm not the one making the decision there. The people who are doing the polluting have the right incentive, and that's what matters.

If the amount of the tax were fixed, the dividend would decrease over time, but the tax gradually increases as we get better and better at doing things without emitting greenhouse gases. The eventual target being net zero carbon. Based on the tax level in the Energy Innovation Act as an example, this is predicted around 2050.

Poor people can still vote. And they will vote against anything that reduces their dividend, even if means voting against things that lower emissions.

As to your second point - moving the goalposts every time progress is made eliminates any incentive to improve. If you're committing to keeping the dividend the same over time, that means you need to keep the tax take the same. And if you're gonna take the same amount of money off me regardless, why should I pay attention to my emissions? In the limit case, of zero carbon, the carbon tax rate is infinite and you're taking a bunch of cash off people for nothing. Somewhere along the way, something has got to give.