Such regulation wouldn't make an iota of difference. It wouldn't shrink any pool, it wouldn't drive wages up or down, it wouldn't do anything.
A type rating is nothing more than a ride in the airplane that meets performance standards, and this can be given during initial or recurrent training. Weather becoming SIC for the first time, upgrading to PIC, doing recurrent, whatever, everybody goes through systems, through performance, through ground...little extra is required to obtain the ATP in the simulator following ground. It's done all the time today...I know an individual who just obtained his ATP yesterday doing that very thing.
So what's the difference? Foriegn carriers already require both pilots to be typed. If the training is already given (and it is), we're talking about executing one additional piece of paper to grant the ATP.
If, however, you're talking about the current practice of putting underqualified individuals in the right seat, people with less than 1,500 hours flighttime, I still don't see that setting that as a minimum standard would change a thing. Nothing. The majority of pilots, excepting the entry level regionals, who hire into a seat are above that experience level (leaving aside historical United, where male applicants have five thousand hours and females and ethnics have three hundred...).
As for piston vs. turbine, don't even get me started. I was sickened yesterday to hear an exchange between an aircraft and the controller. The controller cleared the aircraft to XXX altitude, and the pilot asked for higher. He sneered something in a very condescending tone about "that's where the props fly." There's nothing particular about operating a turbine engine that a student pilot can't handle; it's easier in every respect to operate than a piston engine...there's no valid reason based on a pilot's experience that a student pilot can't operate a turbine engine.
Regionals presently do hire at less than ATP qualifications. However, raising the minimum experience level a few hundred hours won't change a thing. Not a bit, nor will it dry up the pool of applicants. Folks will have to tow around a box for a few hundred more hours, or ride around the traffic pattern whopping students on the brainbox with a rolled up sectional for a while longer...but all companies already have more than enough applicants. There has never been a pilot shortage. Never. Nor will there ever be. Finding enough applicants won't be a problem, and raising the minimum hiring levels or standards won't make a bit of difference.
Nice thought, though.