Should stepwise regressions also be avoided for exploratory (hypothesis generating) modelling? In a recent paper,  Andrew Tredennick and colleagues (2021) suggested to use the drop1() function in R for exploratory modelling (that is to generate new hypotheses meant to be tested on new data). Their paper is very interesting but, since the drop1() function belongs to stepwise regression approaches (which are badly looked upon), I was wondering whether this procedure could truly be recommended even in this case?
My guess is that hypotheses generated that way will be shaky, at best. But sometimes, shaky hypotheses may perhaps be acceptable starting points to deepen your investigations on a phenomenon, especially when this phenomenon has seldom been investigated and/or data are extremely costly or difficult to collect.
EDIT: I have deleted the second part of my question because I asked it here.
EDIT 2 (Contextual clarification): Ultimately, my goal is to identify the most influencial variables controlling the biological phenomenon I'm studying. All the variables whose effects I want to explore are theoretically important to explain my response variable (they have already been selected based on my knowledge of the study system), but my sample size is simply too small to include them all as covariates in a single "inferential" model.

I think the assertion that stepwise selection is always unreliable is a bit too strong.
I think stepwise selection procedure can probably be amended to remove some of its weaknesses. One example might be to use a different sample from the same population in each step so that you are not inadvertently overfitting the model, and are only picking predictors or features that result in a model that generalises well enough for a purpose.
As with anything, when we are performing regression analysis, I do not think the notion that there is a "correct" model, or that there are "correct" or "incorrect" variables to choose is a useful one. I generally only care about a model's predictive performance, and its ability to describe the associations between the predictive and dependent variables. In fact, in many cases, the number of models that may produce an acceptable "fit" to the data and provide good predictive performance is probably very large, and it might be useful to think rather in terms of a set of models that are acceptable, and a set of models that are not, with the goal of a feature selection / model selection exercise being to identify a model that is in the set of acceptable ones.
But just my thought as a practitioner, rather than as a "scientist".
PS - I think the LASSO method, or other methods that use penalties and shrink coefficients, might well be slightly better founded, but I am not convinced they solve all of the issues with step-wise in any case.
