Linear Regression as a descriptive model? I understand that linear regression can be used as a descriptive model (also am well aware that the regression coefficients should be interpreted as correlations rather than causation).
So I was having a discussion with my data science manager about measuring the impact of the usage of cash vouchers (which the business occasionally gives out for free) on customers’ profitability and I suggested using the regression model as a starting point to estimate that relationship. I came up with that idea because the model will allow me to see that relationship while controlling for other covariates.
However, he disagreed with my approach as he thinks it’s an overkill since we already know the direction of the impact (negative) and that we can simply look at historical data and measure the impact through looking at the difference in profitability when a customer uses voucher or not.
Is my approach not sound at all? I’m thinking about when do I ever use linear regressions to describe relationships then?
Any input will be greatly appreciated.

You are right. You can't simply look at pre/post data, say "we know the effect of x" and try to infer the effect of a policy. You need to do econometrics to find out the effect, so nothing is overkill about this at all. I can't comment on the specifics obviously, but your approach is more defensible statistically.
