I tried Cookie Clicker Classic, and realised very quickly why it was superseded and had to be improved.
The rate of production is proportional to the number of buildings. Hence, the time taken to acquire each new building is proportional to C/n where C is the cost of each building and n is the number of buildings already owned.
If C were constant, elementary maths tells us that time increases with log(n), or, turning it around, n increases exponentioally with T. Whacko!
Of course C is not constant. In the current version of the game there is an inflation factor of 15%, i.e. each new building costs 1.15 times the previous one. C increases exponentially with n, and this completely overpowers the effect of dividing by n in the expression C/n. Time now also increases exponentially with n, or equivalently we can say that n, and therefore the rate of production, increases only logarithmically with T.
Let's put this in layman's terms. Say you have been playing CC classic for two months, and on the second day (between T = 1 day and T = 2 days) you were able to get 50 buildings. (This is just a guess, I do not know what the actual number is.) How long will it take you to get the next 50? Nearly two days. After a month of playing, how many buildings will you get in the second month? Thirty times as many? Nope. Only about 50. Play for 2,000 years, and you will only get about 50 between the end of the 1000th year and the end of the 2000th year. Although the total number of cookies baked will increase without limit if you let the game run long enough, it will very quickly become too boring to bother.
No wonder Orteil had to introduce building upgrades to double the output, cookie upgrades, dragon auras, wrinklers etc. All they do however is delay the inevitable.
You might think synergies would make a big difference. With a synergy, the output of one building is proportional to how many of another building you have, so the total production now starts to increase as the square of the number of buildings. Instead of C/n we have C/n^2. Sadly, n^2 (n squared) still increases much more slowly than the exponential increase of C, so the production still only increases logarithmically with time.
The effect of ascensions is interesting. I suspect that most people ascend when there is just not enough happening in the game to keep their interest, however they may choose to rationalise it. Each prestige level adds 1% to your production rate (once it is unlocked). Sounds good huh? But it takes longer and longer to get those prestige points, because it's only based on the cube root of the total cookies baked. I have not done the maths, but I am pretty sure that once again they will just leave the production rate as a logarithmic function of time.
As I said, it's depressing if you think too much about it. Maybe I should just play the game. :D
Update: After a bit more thought, I have decided that the effect of ascensions and prestige points is that the production rate is proportional to the square root of time. This is substantially better than log(T), but you have to get very many ascensions , and the maximum number of upgrades each time, before you see this effect.
I won't bore you with the analysis unless someone asks me to.