Is this circuit one or two-port network?
It is possible to connect a source to the "output" port and measure the response at the input port. For example, you'd do this to measure the reverse isolation characteristic of the network if you were considering using it as a filter.
If you connect something other than the source to the output port, it will load the circuit, and the voltage and current at the output port will depend on this load. Analyzing the network as a two-port allows you to understand this effect.
Even if the thing you connect to the output port behaves like an ideal open circuit (for example, an idealized oscilloscope probe), that is only one special case of all the possible things you could connect to the output port. Modeling the network as a two-port allows you to predict the behavior with any linear load connected to the output.
When you model something as a one-port, the internal nodes of the circuit are considered not accessible. Therefore, with a one-port model, you'd have no information about what voltage and current appear at the output port.


One way to think of this, whatever load you connect to the output port "reflects" some signal back to the 2-port. This reflection behavior is explicit if you use an S-parameter representation of the networks in your model, but it is still there regardless (because the different network representations just represent the same behavior in different ways). The "reflected" signal from the load interacts the same with the 2-port as if it were generated by an independent source.