The US is unique compared to other nations...we have a thriving general aviation segment. Our entry-level training system is designed to cater to that...a brand-new US CPL is an adequate qualification to fly a light trainer, but nothing more than that.

Europe does not have GA (except for the ultra-wealthy), so their entire training system is geared towards professional turbine pilots from day one.

If it were up to me, all pilots (PIC and SIC) of large turbine powered aircraft in the US would have to hold an ATP. Then I would raise the standards for an ATP, make it similar to Europe with more academics and theory. Too many US professional pilots have a knowledge of aerodynamics and systems which is based on rote memorization, without actual comprehension of the underlying theory. I'm not advocating requiring an engineering degree, but a little more fundamental understanding of things. Frankly, if you do not understand basic DC electrical theory, you have no business operating an turbine airplane...

Keep the 1500 hours required for an ATP. If it becomes impossible to staff airlines due to too many low timers, you could go to a european-style frozen ATP where you do all the work, take all the tests and checkrides, but do not actually hold an ATP until you get the flight time. You could allow a frozen ATP to sit SIC.

As for additional screening...

Keep all the medical stuff with the medical people (including psychiatric). It would not hurt to tighten up on cardiovascular and body weight...that would actualy force some people to do themselves a favor and live better.

I'm not in favor a formal screening based on academics, although it would probably be a good idea to have a screening test for professional applicants...kind of like MCATs. I would not want to exclude somebody based on high school academics, give them a chance to grow up and develop the initiative to meet the standards.