[downandout]

Most e-commerce sites use the Facebook pixel - they'd be crazy not to. Retargeting is actually where most e-commerce profits through Facebook ads come from. Advertising to cold traffic is often a loss leader, just to get an audience to retarget to. They lose money getting people into the top of the funnel, and then make it back as a smaller number of people progress to the end of the funnel.

So no, sending your data to Facebook isn't dumb, and in fact, it would destroy most smaller e-commerce businesses if they couldn't send their data to Facebook.