I am not sure including the GFC decline helps selection of a screen that will perform in the next major decline. I can only think that something like BCC protects you in a decline and then select screens that do well in a bull market.

Absolutely.
These are wo different things.

I just find it annoying and not helpful when somebody presents
"WOO-HOO!!! This screen does fantastic (in a period which is a bull market)."
Duh. Just about everything does great in a bull market.

If a backtest DOES include at least one bear market and a couple of correction markets, *then* it attracts my interest.

But most people don't use any sort of robust timing scheme to sidestep the full depth of a bear market.
That's assuming that there IS such a timing scheme.

And I don't generally come across a backtest that even contemplates a timing overlay.

Usually when I want to do that, I download (if possible) the daily/weekly/monthly values of the backtest into a spreadsheet and then apply my own timing scheme to it.

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