Would Vulcans really make First Contact immediately after Earth has FTL

Anyone else think it's a bit odd the Vulcans make contact with Earth immediately after finding out they have FTL technology just because a ship happened to be passing through the area at the time?

I mean do all Vulcan ship captains have permission to make first contact the moment they find out a previously pre-warp world has FTL? Shouldn't have to like report that to their government first and then get official permission to make contact? And wouldn't the government take some time and talk it over before deciding to grant that permission?

Also, shouldn't there be more factors involved in deciding to make first contact then whether or not a planet has FTL technology? The movie said "WWIII" had just ended and the planet was in a state of near-total anarchy and chaos. You'd think the Vulcans might be a bit reluctant to make contact on grounds that one guy creates a primitive warp engine.