It boggles my mind how you come to your conclusions...

You say happiness will be better suited for all map sizes & show your logic by showing the changes to the policies.
Because the
general principle is much easier to tweak and balance. It obviously needs testing, but let us see how it would fare compared to today's standards.
Currently, huge map policies costs an additional 15% per city.
From the new patch this number will be 7.5%.
Currently, each city costs 1.2 happiness on a huge map (2 on standard size) or 60% of the original.
From the new patch this number will be 1.8 (60% of 3).
Today:
+15%

needed per city
-2.2 unhappiness per city (city + 1 citizen).
New patch:
+7.5%

needed per city
-2.8 base unhappiness per city.
Lets say you want to expand, today, to 10 cities on a huge map with the first three social policy branches. The only policy that offers happiness is Meritocracy, a whopping 0.5

per city. The only policy that offers culture is Liberty, a whopping +1. Everything else must come from a Colosseum, Circus, Monument or Temple. You can obviously go Tradition, but we talk about really large empires.
***
From the new patch, it will be easy to expand with Honor. Honor will offer culture from barb kills (easy to get on huge maps, yes?), Military caste and Professional army will offer a total of +2

with a garrison and city walls as well as extra +2

.
From there you can go Piety (still killing barbs), build a few monuments (15% cheaper due to Piety starter) and receive further +1

+2

per city. At this point you become happiness neutral (at population 1) and have +4

per city and +3

per city from policies and a monument.
You can place an almost indefinite number of pop 1 cities this way, whithout even touching luxury resources, colosseums or circuses.
Now lets add a colosseum +2 happy. A temple, +1 happy. Add a castle +1 happy. A stone works or circus, between +1 and +2 happy.
We're still in the medieval era and we can already have cities with population 6 or 7 without even dipping into luxuries.
As long as you build a monument, have a scout garrison (you can take Oligarchy as well) and if you dip slightly into luxuries you can place an infinite number of size 1 cities and build from there.
... and build from there. That's the idea I like the most.
Honestly, I presume the devs planned the new happiness system around players having at least 3 full policy branches before hitting industrial. And whatever way you go, you'll end up with +4 to +6 happiness per city from branches alone.