Subsequent modifications would of course invalidate any digital signature you’ve applied, but that only matters if the recipient cares about your digital signature remaining valid.
Put another way, there’s no such thing as a true read-only PDF if the software necessary to circumvent the other PDF security restrictions is available on the recipient’s computer and if preserving the validity of your digital signature is not considered important.
But sure, it’s very possible to distribute a PDF that’s a lot more annoying to modify than your private source format. No disagreement there.