While I seldom agree with tuft, your suggestion is not practical. In some worlds, owners simply carpetbomb the entire world with crappy offers. They don't deserve a prompt response.
If I had my way, you would be unable to make a trade offer until an exchange has taken place. One owner initiates in TC, the other owner responds. Until then, no blind offer. Do you think the Oakland A's just send the Dodgers an offer for Kershaw before even asking LA if they're interested?