Yeah I agree with those points, it doesnt have to be that way even if you get stuck with your policy choices.
It's just that civ 5's take on it was way too imbalanced, really (as well as having too few opportunities to max out different trees).
Fun fact, I started up my first civ 5 game in several years yesterday.
Went Maya (I figured an OP civ would help when being this rusty on deity) and had the most ludicrously strong start on a vast stretch of desert floodplains with Mt Sinai (+8 faith) right next to it, letting me pick Desert Folklore right from turn 5 (I told you this was a good start..).
It's also up in the corner of the map with only two neighbours, which means I have lots of space to myself to freely settle.
Then came the problem - should I start Tradition, Liberty or Piety?
On paper you'd think that the Mayan would be perfect to go Liberty (spamming lots of cities with that fantastic faith/science building at it's base), or Piety (focusing even harder on religion, since Desert Folklore + huge strip of desert Floodpains to fuel massive faith).
However, I just can't in good faith pick Liberty or Piety.
While the desert landscape is absolutely fantastic for faith and growth, there is only one luxury - incense.
I could settle away from the desert to get more luxes, but there are only a maximum of 5 different luxuries in the area, and that can't support 6-8 cities wide Liberty.
Piety is even worse off because it has no happiness policies at all, so I get doubly punished if I try to settle the desert area.
Also two of the unique luxures are close to one of my two neighbours, Attila (the most dangerous early neighbour imo, bar none), and neither Liberty nor Piety have any defensive bonuses to justify grabbing city space right in his face.
So, even though I have fantastic landscape for a religious game, and massive space to settle wide, I feel like I have to default back to Tradition because it's the only way I can get enough happiness, gold and defensive power to stay afloat.
And while I would love to go Tradition + Piety or Liberty + Piety to really benefit from Maya, that's a no-go because of how few times you can realistically pick policies (Rationalism is almost mandatory after all) before ideologies (100% mandatory).
TL;DR: It's bad game design when even the civs that apparently are designed for different playstyles, all get shoehorned into the same cookie-cutter build.
And this is why I don't play Civ 5 anymore. The entire game is ruled by Global Happiness and the punishment of any attempt to expand, be it peacefully or warlike; through Global Happiness hits, increasing tech costs, increasing civic costs, civic imbalance, and so on and so forth.
The Civ 7 civic/culture system should look to Civ 4 and Civ 6, and as far as I'm concerned they can - and should - completely ignore Civ 5.