That happened many times in the US and in other countries which is what led to the initial float of the dollar by Roosevelt. It definitely worked at the time, with the influx of money reversing the huge deflationary pressures that were prolonging the Great Depression

You could argue that deflation like that is worse, and in many ways it is. But when the dollar is allowed to be devalued consistently for 53 years like it has been, you have issues like housing costs. Median home price pre "Nixon Shock" was around 24k, and has increased 20 times that since, while the median household income has only increased by 10.

As you said, the consistent increase in the population would require the gold supply to remain above a certain threshold, and I wouldn't trust our federal reserve banking system to be able to manage that, nor would I trust other nations to play nice. With how large our trade deficit is, it wouldn't be long until hostile nations drained us of all our gold and collapsed our financial system yet again.