Price time series are not stationary. So we difference them and get the return time series, which are stationary. Does this mean, it is always a good idea to model only the return series of financial assets.
Alternatively, do we not need to model prices ever ?
Always - may not be!
It all depends upon what you want to do with the data, e.g., if you want to run autoregression (ARMA/AR/...), then yes stationarity plays a big role because it implicitly limits the effects of data that are far away from the current data. Check for yourself, run a AR(1) model, and see how the error is propagating.
I guess, you want to predict future values of stocks/options or any underlying. There are statistical ways of doing this such as modelling as financial time series, and run regression but also you can use stochastic calculus to model them and almost always price return series is used.
Coming to other side - no we do not always hit the return series modelling. For instance, in Artificial Intelligence side of modelling (Recursive Neural Network, Echo State Network etc) we may use return series or raw prices. And why we use return series - because it is bounded (well most of the time), behaves well and friendly to mathematical formulation in A.I context!
The benefit of return series:
Think about the mean of the the last 100 trades, you take raw price and take return series. First one gives you a value (say USD $30$), but return mean will most of time hover around $0$. As time goes on the mean of the first value will keep changing but the mean of the return series will keep hovering around $0$. This connects itself to something known as "homoskedasticity" of regression. So if mean is changing with time (for raw price case), and you run a regression on the raw data, the result will be spurious as it directly contradicts with the assumption that error is normal with zero as mean and a constant number as variance (most of the cases).