Sorry, but it's not all ridiculous, overblown stupidity anymore. Some of these people seem stupid enough to actually follow through on their threats.
I understand the scariness of receiving such a thing, but is there any evidence to suggest that the person willing to act on such a threat is influenced by (1) inability to send or (2) confirmation of receipt (or lack thereof)?
Separate from that question, how and why is it better than the intended recipient knowing credible threats have been made on their life? When is denying them the agency to decide how to respond to the threats acceptable? Does it accomplish anything but alleviating the mental turmoil associated with understanding the realities of their own life?
I'm not denying that the scale of the problem has grown to the point that rare events (someone following through on Internet bluster, in this case) will occur. I'm simply remembering a simpler time, when people didn't clamor for the sanitization of their daily Internet lives.
It's also not as if the only two possibilities are “actual stalker attacks you” and “nothing happens”. SWATing, spamming friends/family/coworker with hateful propaganda or photoshopped porn, placing embarrassing ads with the victim's actual contact info, etc. are all things that happen in the real world and don't require some blowhard to leave their house or risk persecution anywhere near as much as a serious physical attack would entail.