Why is the Hybrid-PI model like that?
To quote George Box, 'All models are wrong, but some are useful'.
We use models to simplify a complex situation. The model preserves some aspects, while approximating or ignoring others.
There are two main models most people use for BJTs, the voltage controlled model and the current controlled model.
When biassing a transistor, the current controlled model tends to be most useful. This has a diode between base and emitter, the collector current is beta times the base current.
When operating the transistor as an amplifier, the voltage controlled model tends to be the most useful, with the collector current gm times the base voltage. This gm will be a tangent linear approximation to the actual V/I slope around the particular bias point of the transistor, which is why we bias the transistor first, then use the gm model.
In addition to the basic model, we can extend it to higher frequencies by adding some of the main parasitic capacitances, and incorporate Early effects by adding output impedance.
At some point, it's useful to stop elaborating the simple model. The test is not whether the model is accurate, it whether the model is useful. When we design microwave circuits, we tend to measure the S parameters of the transistor at a particular bias point, rather than relying on a theoretical model that we hope will be accurate from uA to mA, and from DC to light.