I infer that slavery is the device which turns food into production. Is slavery something so crucial that it should be kept over the whole game?
Slavery is the single most powerful component of Civ IV. How long you use it the game is very dependent on the type of game you are playing, but typically no matter the gameI play I will be in slavery for much of it, with short-term switches to caste system during Golden Ages.
If your desire is to get better at the game, move up difficulty, and really master, you will learn how to whip and whip effectively. It's not just a matter of just whipping stuff cause you can.
I have been spamming many of the same building in every city that had decent production as Willem (granary, barracks, stable, forge, library, temple, market, grocer, aqueduct, colosseum, lighthouse, harbor, customs house, theatre, courthouse, jail, university, observatory, dike, factory, coal or hydro plant, hospital, airport, recycling center, public transportation). My production always seems to outrun my research so that I keep running out of buildings to make, even at 90% with cottage spam.
What I take from what you say here - and it is not a criticism, but very common with new players - is that you are "going through the motions". You are playing the long game but not really playing to win the game. Just building buildings is not proactive. My assumption is you are likely playing into the 20th and 21st centuries with no real goals except maybe space, or losing to an AI winning by space, culture or diplo/domination circa this timeframe. That is all fine and well, you are new, but the idea here is to set goals earlier and win the game. I'll will list a high level course of action:
1) Strong early game focused on expansion (6 or more cities by 1AD) and strong mechanics (economy building, worker management, diplomacy and maybe warfare)
2) 1AD or sooner you have an idea on how you want to win the game (exception - culture is a special type of VC and if going for it, optimally, I do the things needed from the start, unless using it as a fallback VC later)
3) Plan and Act toward that goal
To put this in perspective, since perspective is important and as a new player to the game, your's is different, I will give a hypothetical. Let's assume you are playing standard settings/Noble/Pangaea game. Based on what you've said, you are either losing or otherwise playing into the 21st century and either winning/losing. Now just to show you what could be done at Noble level with experience, my expectation would be to win the game militarily in the BCs. That is very much a possibility. (ofc, one could win anyway the want here, but just an example for perspective. Regardless, experienced players would win whatever VC here much sooner than some of the buildings you mention are even teched.
On the other hand, I would mention that anyone can play the game how they choose. Play the game casually just for fun and build whatever they desire. But most here giving you advice are from the standpoint of helping you win, win faster/better, and move up difficulty. My guess is that is what you want to do by virtue of your questions.
So, what do you do besides building all these buildings we say not to build? That really is the question now.
1) Build the best wonder in the game...an army to go kill peoples
2) Build wealth or research to push teching to that critical military tech, then go rush an army and go kill peoples.
3) Kill stuff and the peoples that own the stuff
4) How about expanding more so you can have more cities and; thus, more production to build units to go out and kill peoples.
5) If you have marble or stone (or IND trait), put hammers into related wonders for fail gold. Fail gold allows you to tech faster so you can kill more peoples with your big tech lead - and pay the people killing army
6) Build Wealth
7) Enjoy a nice Chianti