There are several reasons that you cannot just count the number of times your server has served the page.
The biggest is bots - on my site (and I assume most others), legitimate requests are far, far outweighed by bots. Sometimes you can tell that they are bots but it is very common for bots to pretend to be real users. Oftentimes you can't tell from a single request but only but looking at the pattern of requests.
Some bots do take the trouble of running scripts on the page but thankfully they are in the minority so far.
Caching would certainly break the system as well, in the other direction.
The biggest is bots - on my site (and I assume most others), legitimate requests are far, far outweighed by bots. Sometimes you can tell that they are bots but it is very common for bots to pretend to be real users. Oftentimes you can't tell from a single request but only but looking at the pattern of requests.
Some bots do take the trouble of running scripts on the page but thankfully they are in the minority so far.
Caching would certainly break the system as well, in the other direction.