This topic should not be about whether a right way to play civ exists, or what it should be. The question is if the perfectly ordinary and common game strategy of "build T3 buildings" is on-par with other options. I think it's non-controversial to say we'd all prefer it to be at minimum generally balanced with other options, just like we'd prefer the civs and different districts to be generally balanced, right?
In that case, let's look at the most straight-forward lineup, the Commerce buildings, where we can most directly compare production/purchase costs to their yield.
Note: All building yields can be doubled by respective policies in tall cities with good districts, but this affects the yields of all buildings proportionally. Hence, it does not really alter analysis we make here.
Market:
Cost: 120 production (480 gold)
Benefits:
+3 g/t
+2 g/t per 3-envoy Trade City-State
+1 gpp/t
+1 specialist slot
+1 trade route slot
+1/2 progress towards the Guilds Civic (=77 Cul each for building 2), pivotal in all paths. (ALSO essentially gives progress towards Medeival Faires!)
A 0 City-State Market pays for itself in 160 turns. If built on turn 100 of a 300 turn game, it will yield a net profit of 120 gold and 200 gpp. If you built primarily it for only 50 turns of gpp, you paid 330 gold for the privledge.
A 2 City-State Market pays for itself in 69 turns. If built on turn 100 of a 300 turn game, it will yield a net profit of 920 gold and 200 gpp. If you built it primarily for only 50 turns of gpp, you paid 130 gold for the privledge.
A 4 City-State Market pays for itself in 44 turns. If built on turn 100 of a 300 turn game, it will yield a net profit of 1720 gold and 200 gpp. If you built it primarily for only 50 turns of gpp, you still profitted 70 gold.
All of this is ignoring the elephant in the room: You also get a TRADE ROUTE SLOT, which is a HUGE perk offering large, highly-scaling profit margins and secondary benefits directly applicable to every victory condition.
What a slam dunk. Decent payoff, amazing with city states and hitting 3 envoys is trivial. Around for the entire game. Progress towards two key, unavoidable Civic. And, of course, the invaluable Trade Route slot: a reward on par with a lesser wonder or great person.
Bank:
Cost: 290 production (1160 gold)
Benefits:
+5 g/t
+2 g/t per 6-envoy Trade City-State
+1 gpp/t
+1 specialist slot
+1/2 progress towards the Economics Tech (=194 Sci each for building 2), which gates Interchangable Parts
A 0 City-State Bank pays for itself in 232 turns. If built on turn 150 of a 300 turn game, it will yield a net profit of -410 gold and 150 gpp. If you built it primarily for only 50 turns of gpp, you paid 910 gold.
A 2 City-State Bank pays for itself in 129 turns. If built on turn 150 of a 300 turn game, it will yield a net profit of 190 gold and 150 gpp. If you built it primarily for only 50 turns of gpp, you paid 710 gold.
A 4 City-State Bank pays for itself in 89 turns. If built on turn 150 of a 300 turn game, it will yield a net profit of 790 gold and 150 gpp. If you built it primarily for only 50 turns of gpp, you paid 510 gold.
Ok, this is... much worse. No trade route, an important but less key boost, and the City States now require a far less trivial 6 envoys. Yet compared to a Market the efficiency is less than 50% for gold, and even less for gpp! It's a long payoff, and without 6-envoy city-states, we might not even make our costs back before the game ends!
Stock Exchange:
Cost: 390 production (1560 gold)
Benefits:
+4 g/t
+7 g/t if powered
+1 gpp/t
+1 specialist slot
+1/3 progress towards the Capitalism Civic (=208 Cul each for building 3), a less important leaf tech
An unpowered Stock Exchange pays for itself in 390 turns. If built on turn 200 of a 300 turn game, it will yield a net profit of -1160 gold and 100 gpp. If you built it primarily for only 50 turns of gpp, you paid 1360 gold.
A powered Stock Exchange pays for itself in 142 turns. If built on turn 200 of a 300 turn game, it will yield a net profit of -460 gold and 100 gpp. If you built it primarily for only 50 turns of gpp, you paid 1010 gold.
Power typically costs some combination of tiles + build charges, power plant production + resources + CO2 output, or hydroelectric dam production. While it's hard to compare, 1 power infrastructure roughly ballparks to 100 production, or 400 gold.
A powered Stock Exchange pays for its true cost in 178 turns. If built on turn 200 of a 300 turn game, it will yield a net profit of -860 gold and 100 gpp. If you built it primarily for only 50 turns of gpp, you paid 1410 gold.
Now this is a train wreck in comparison. It is far less gold and gpp efficient that the Bank, is connected to a far worse boost, and is dependent on power infrastructure. Yet this dubious investment can only be build late game? It is almost certain we will not be getting our investment back before the game ends.
While the Stock Exchange is an especially bad case, all (non-holy) T3 buildings follow similarly unappealing math. Unless you are after the quick Research Lab boost or the Broadcast Tower GW slot + Rock Band bonus, building any of these 3 buildings (And possibly Banks) is simply mathematically incorrect for almost all cities in almost all situations, and those exceptions probably all involve tall Pingala or World Congress building bonuses. There is almost always a cheaper, more efficient investment available--either projects in the short-term, or expanding wider in the long term. Military Academy and Seaport are also overpriced for most situations, but at least require no power, offer a nice +1 Housing, enable special military production options and XP bonuses, and Seaports even add a sweet tile gold bonus that is usually single-handedly more than a powered Stock Exchange! As such, there is still plenty of situations where they are worth considering.
Edit: Airport is also a wild 600 production for +3 a turn. You are really just paying (a steep prmium) for the +XP bonus and airlift ability.
Edit 2: Oh yeah, there's always that CRAZY Dark Age policy. You know the one. If it is on the table, sure--Stock Exchanges are nuts and all bets are off.