Often you will go after average partial effects in your sample. Or you have some correlated variables in mind such that you can just plot the partial effects. Sometimes you have different models, where you will plot a distribution of partial effects around a mean based on some prior assumption...
I mean, it really depends. If you impose a more complex relationship, then of course you can not put everything in a single number. But no matter what you are interested in, such a model will give you the possibility to exactly determine the measure.
And what you are saying is also not correct. I may very often be interested in fixed values. Doing this regression, and not a quantile regression, for example, means I am somehow interested in a conditional expectation. That means I probably care about some sort of average impact, perhaps for some fixed subgroups. But those averages are fixed values...
I think the point is that in these models, we know exactly what we go after, how to get there, and what it means. We know exactly when our inference may fail.
If we both care about average effects, and I can convince you of my identification assumptions, then there is really no mystery left as to what my estimates mean.
In with Deep Learning, this is still more difficult.
This is the problem the poster originally pointed to - interpreting a variable conditional on the fixed values of all others doesn't always make sense when there's strong correlation among predictors.