Why RMS value used in transformer equivalent model?
There are several ways to describe an AC waveform. We can use the rms (the heating power), the peak, the peak-to-peak, the average of DC. Each representation will have its own advantages and disadvantages, and situations where it's more appropriate. If we know the waveshape (and if that's not specified it's usually sinusoidal), then it's trivial to convert between any pair of numbers.

Customarily, meters are calibrated to read the rms value of a sinusoidal waveform. If the measurement type is not specified, then it's usually rms.

If you are analysing a transformer on the basis of output as a function of input, it really doesn't matter whether input and output are measured in rms, peak, or any other consistent way, the ratio will be the same.

If you're analysing a transformer relating flux to input voltage, then it's true that measuring flux as peak is more useful. However, as flux is the integral of voltage, we need to know the entire waveform of the input voltage, not just a single number like peak. For instance a transformer with square wave drive will have a different peak_volts to peak_flux relationship than one with sine wave drive. Whatever number we use for input voltage, rms, peak or anything else, will need to be interpretted through the waveshape and Faraday's Law to arrive at the flux.