I'll admit, my current computer doesn't have an A-drive. I have one I bought at a clearance, and could wire that in. Or, something else. But like you say, not much sense keeping them.
For sure, I wouldn't want someone reading my data, I do have access to a burn barrel.
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What's the point in keeping them? When was the last time you saw a new computer with a diskette drive?
Depending on what's stored on them, though, you might want to either securely erase them, or physically destroy them, instead of just putting them in the trash -- any sort of financial data, medical records, other personal information, plans for building nuclear warheads, etc.