Why won't on-line pharmacies accept pre-paid Visa cards as payment?

I have tried several and they want my bank account or a credit card instead.

And I will only limit my liability to a fixed amount on the pre-paid card.

It makes me think they are crooked.

Are they?

Check with this post.
https://www.giftcards.com/gcgf/giftcards-not-working

As the link tells you deep down: register the card with issuer so that your name and address is associated with it. This cuts down on certain scams the retailer is trying to avoid.