Wow. Fascinating topic. Where to start?
How about first of all, the Population number of the City makes no sense from day one, even in civ terms. The city centre tile is being worked and one tile in the field is being worked, so by internal "civ logic" the "true" Population is actually 2 on city founding, not one. Of course, no other game mechanism recognizes this other than the tile working/yield production mechanism.
Then there's the question of what form population growth took in the real world, under most conditions. It probably looks close to the Civ representation, i.e. slow linear growth, until the health revolution. Someone will no doubt cite studies I don't have time to look up right now.
So then we get into questions about what factors truly determine how fast the population grows? Civ 6 has the most complex formula yet, using the traditional food production (but only locally, 'cuz "civ mayors don't share"), the bizarrely named "housing" (which includes the benefits of medieval walls and plumbing), and "amenities" (which is "happiness" in everything but name).
The real world factors likely line up behind available food (and Victoria's right, once basic food needs are met, pop growth isn't faster with surplus food) and mortality rates (more wars = slower pop growth, better health care = fewer infant deaths = high pop growth). So as a game mechanism, some simple way to measure food availability and general population health isn't bad. Food does that, and "housing" kind of does that, though in a mostly silly fashion in Civ 6 (anybody really think you should be able to grow a big modern city without investing in Sewers? and if so, maybe a Tourism hit would be in order?) Not sure amenities/happiness should play into it at all (less entertainment options likely mean more babies - check out stats from black outs).
In terms of game play, linear population growth is likely easier to balance, so mechanics that cause your population to growth gradually over time and avoid "snow balling" probably makes for better overall game play.