I am reporting the results of an analysis where we tested the effect of various demographic predictors on the number of counselling sessions undertaken by participants during a clinical trial. I ran a Poisson regression with number of sessions as the outcome variable. To control for exposure I included an additional predictor, the log of the number of weeks each person was enrolled in the trial.
I have read e.g. here that including this offset variable effectively turns the count into a rate.
My questions is rather than including the offset variable as a predictor, why not simply convert the count outcome variable itself into a rate?
For example in my study I could just divide the number of counselling sessions by the number of weeks attended. Is there a good reason not to do this and instead use the offset variable?