Seasonality and ARCH on Trend Models

It seems there is the need to check for seasonality and ARCH once we find proper AR(p) model.

However, I haven’t seen any mention of the above tests to Linear Trend or Log-Linear trends Models.

Why don’t we check for seasonality and ARCH on trend models? It looks like we just check for Serial Correlation and if there is none, we can go ahead and use them.
Thanks