I'd do so where I live, I've never had the postal service here loose any mail. I could even pay 5€ extra and the insurance for the mail contents would cover if the 5000$ vanished, in the unlikely event that happened. Tbh, amazon delivery is less reliable than the national package delivery.
Yet it's safe enough to send those 1,200 dollar stimulus cheques, right?
The point is that a check can be reissued, and generally speaking, there’s a system of validation to prevent unauthorized use. Cash and votes have intrinsic value.