Most theme parks in the US are paid entrance too. Although there are some with free entrance, this model is more for carnivals/fairs/etc.
The game uses pay-per-ride because it adds a little more depth to managing your prices. The game is also not very well balanced so charging per rides makes wayyyy more profits.
However, it is possible to sustain some income with paid-entrance and free rides if your park is big enough. But it will always be more profitable to charge for both
Id like to see the devs balance pricing/economy a bit better, but not too sure if that will happen (certainly not anytime soon)