Yes, the reputable cadet programmes train an ab-initio student through a programme leading to the role of first officer for the partnered airlines. The training is monitored, and specific. The selection process starts at onset and the ongoing standards are monitored throughout the basic training, intermediate training and on to the advanced training at the airline itself. The airlines requirements are easily and quickly fed into the relevant programmes as and when required.
One of those requirements (that even in the last week) is being fed in, is either the introduction or improvement of Psychometric testing and evaluation at introduction and throughout those courses.
The problem with the FAA requirements are that they are specific to that country. There are many things that may work fine in the US domestic arena that simply do not outside of it. R/T standards, Land & Hold short procedures, etc. The USA has a vast resource of general aviation and within that resource the ability to set benchmark levels for "minimum experience." It also has a large resource of military career changers.
The system (in the US and elsewhere) was never designed to push 250/350/450 etc. hour G/A pilots into the right hand seat of an airliner. Nether was it in the UK and many other countries. In the UK the minimum level of quantitive hour experience for obtaining a commercial pilots licence used to be 700. Few pilots at this level would have been recruited into the right seat of jet airliners the typical minimum tariffs being in the order of 2000-3000 hours. Even then, the wash out rate or retesting rate was significantly high.
Throughout this same period there were a limited number of "approved" training programmes (utilised by some of the larger airlines) whereby an ab-initio pilot could be trained from scratch over a period of two years towards specific airlines cadets programmes. These programmes have been in existence for at least the last half century, providing excellent pilots who have completed full careers in many cases.
During the last decade changes to the licensing system in the UK and Europe (as a result of "harmonisation" between member states) brought the licensing system more in line to that in the USA and elsewhere. In other words the CPL was a G/A "aerial work" licence in many respects. The old "approved courses" didn't change very much other than in one very crucial respect. That being the number of them expanded as did the number of airlines who chose to utilise them for their own new cadet programmes. As a result of this combination you ended up with thousands of new "self improver" CPL holders who all believed their 250 hour "lo-cost" licence would provide them the same opportunities as the old 700 hour licence. It didn't! Not only that, but the expansion of the cadet programmes simply squeezed out the more experienced pilots who might once have seen their "stepping stone" careers rewarded by reaching the 2000 hour plus plateaus.
No matter how many times you point out these inconvenient truths some people still stick their fingers in their ears and continue to chant their own mantras, in the hope that it might all change tomorrow!
The FAA "1500 hour rule" was itself something of a non-sequitur following the Colgan air crash. Neither of the two pilots involved had anything like that level of experience and it was never proffered as causal or contributory to that accident. However, poor training and fatigue were proffered as causal and contributory, neither of which a "1500 hour" tariff would address.
In the US it is very unusual for an airline to employ somebody without a college degree by virtue of that countries education system. In the UK you would likely lose more than half of the current airline pilot workforce if there was a similar requirement to hold a college or university degree. Strangely there is no vociferous call for an emulation of the US standard in this regard!
The common mistake on these forums is for people to confuse the structured and specific airline cadet training programmes, with the general requirements for a basic Commercial pilots licence and think they amount to the same thing. They never did, and they don't now. To that end raising the "non-approved" requirements for airline employment to the holding of a full ATPL (Airline transport Pilots licence) would be fine. In reality it would make little difference to what happens now and what has always happened. It would however focus the basic airline requirements on those seeking to achieve their ambitions outside of the full time intensive cadet programmes.