Let's assume $p$ potential predictor variables $X_1,...,X_p$ and a single dependent variable $Y$.
Now I evaluate the performance of all possible linear models considering all possible combinations of predictor variables ($2^p-1$). The performance measure(s) could be pretty much any statistic but first comes to mind $R^2$, $F$-statistic and MSE. Based on them I select the "best" model or the top selection which I can check out more closely.
Intuitively I would assume this is a great idea—but I read around a bit and came across the infamous concept of "stepwise regression" and how it is considered useless by a lot of ( though apparently not all) statistically trained people. The reason seems to be that the assumed distribution underlying the involved statistics does not hold for the scenario.
But stepwise regression is usually described as a slightly different algorithm where you start with a model, adding and removing variables from the model based on a criterion for a statistic.
So my question is whether the approach I describe would also be a type of stepwise regression and hence be handicapped by design. On the latter part (if it is SwReg) I would be interested in clarification on where the handicap comes into play and whether it is possible to amend it.