Yes, it does contribute to the pressures on the natural world.
But while the global population is rising by 1% a year, consumption is rising by 3%.
That's the biggest issue.
No, it is not the pre-eminent issue.
It is often used as a way of displacing blame:
"It's not us consuming, it's Them breeding."
This displacement, I believe, explains why the issue is over-emphasised.
In rich nations, where longevity is rising but the birth rate (mostly) is not, almost all the talk is about birth rate, and you seldom hear a word about longevity.
I wonder why.
While few governments want to raise the birth rate (and some seek to reduce it), almost all governments seek to raise the consumption rate. Growth is their overriding aim.