Broad search has a place
It works when the user still needs orientation and does not yet know the right category.
Comparison article
AllChinaBuy Spreadsheet page or broad search: which one fits better?
The answer depends on how much you have already narrowed things down. Broad search is good for discovery. Category pages are better when the choice is already clearer.
The best page is the one that matches how close you already are to making a choice.