> A key factor contributing to climate change is the number of people weighted by energy consumption.

It is sometimes framed as I=PAT equation. https://en.wikipedia.org/wiki/I_%3D_PAT

It's probably important not to take that equation too seriously, as it's roughly an accounting identity based on structural assumptions. If you don't like it, pick any other factors to factorise one side of I=I. But it does provide a helpful perspective: in terms of what you stated, we'd also need to multiply by a coefficient that describes carbon emissions in terms of per-capita energy consumption.

> Should governments in rich countries encourage people to have fewer kids or otherwise constrain their life choices in various other ways? This goes against liberal values. What do most progressives think?

I'm not sure if I am a progressive. My short answer is "yes, governments should constrain life choices to help force a controlled crash ahead of continued overshoot then a forced hard collapse". In the future I suspect we'll end up in scenarios where either we have the luxury of choosing one or more ecologically incompatible liberal values to break, or reality will go on ahead and break one or more of our incompatible values for us.

A liberal perspective of free individual choice in the short term that causes uncontrolled growth and consumption at the population level is not logically compatible with a desire to avoid wide-scale suffering due to famine, resource war, etc in the future (assuming that the latter concern is a value we wish to maintain).

Specifically regarding population, the carbon emissions of a US family* + descendants versus a Bangladeshi family + descendants, projected forward 100 years, estimates that the US family & descendants generates about 40x as much carbon emissions. (picking those two countries as extremes of (high per-capita pollution, low population growth) versus (low per-capita pollution, high population growth)). The US family & their descendants still incurs a higher carbon emission footprint even up to time horizons of 900 years. This is even with a US birth rate of 1.9, which isn't sufficient to maintain population over the longer run.

From an overall population level, arguably "we" the human endeavour should seek to minimise the number of people with affluent high-pollution lifestyles.

On the other hand, of course there is no "we" that includes all of us. Perhaps myself and my neighbours can figure out how to push more of the costs of global warming onto you and your neighbours while keeping a disproportionate share of the benefits, or vice versa. Or maybe together we can collaborate to share the benefits of the current cheap energy jackpot and push more of the costs on to our actual/hypothetical grandchildren.

* i dont mean to pick on the US, I'm australian, we're about the same or worse in terms of per-capita impact of ruining your children's atmosphere and climate. you should impose trade sanctions on my country to encourage my government to stop pushing for new coal mines. my federal government can't seem to think of anything cleverer to do than digging up all of australia's coal and selling it before it loses all market value.