It isn't that hard to know where your protective gear stays and have it handy. Consider keeping it close by when the weather forecast is unfavorable, a time when you might take other precautions (something like Wildman's HurCon scale).
I don't keep a first aid kit in every room in the house, but I always have one in my briefcase and another in my backpack. A third formal kit is in my waist pack when on the bike. I always have band-aids in my wallet. More and more often I carry a set of nitrile gloves together with a bandanna in my hip pocket.
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Geezer in Chief