C525 vs C560
Two weeks training in both, at the end of the C525 you go home with your C525sp type...which is valid forever...
At the end of the C560 training, you get your type...your crew mate goes home to fly in a crew...you now start another week of SP training...you now demonstrate everything possible as a single pilot, including raw data single engine approaches, ect....
I "demonstrated everything possible as a single pilot" during me CE525S initial, including OEI raw data approaches - it ain't exactly hard for a professional pilot and even less so for anyone with any previous experience in 500-series Citations.
Your first SP type, has to be done in the aircraft, not a sim...which means that if you fail, about a 50% failure rate, means coming back a month later...and doing the whole flight again...not in a sim and do the failed portion after having a cup of coffee in the lounge.
I had a good friend get a CE525S type rating, with his training and type ride in the actual airplane, in TWO DAYS. Granted he had a CE500 type and a couple thousand hours in it, but again - not exactly requiring of Bob Hoover airmanship. The guy I fly with also did his CE500 training & type ride in the actual airplane - but that was a 7 day initial.
Only 120 or so pilots on earth have the exemption every year....roughly 500 pilots have ever had the exemption..with most not exercising SP privileges....they just do the SP training as recurrent...but have a copilot...
So the difference is because the FAA has this phobia once you get into planes past the 12500 lb limit...so when you start getting close to 17000 lbs, and the speeds his . 77...they want the training and records requirements.
That "phobia" you refer to is called Part 25 Transport Category Aircraft certification requirements, vs. Part 23/Commuter Category certification requirements.
CJ3 has a MTOW of 13880; the CJ4 you mention is in the 17k weight class with a MMo of 0.77M - faster than any 500-series airframe.
Premier II has a proposed takeoff weight of 13.8k lbs. HBC still plans for it to use the RA390S type rating of the Premier 1/1A, so no "exemption" will be required.
The Phenom 300 has a MTOW in the 17-18k lbs class and 0.78 MMo , and it too has a single pilot type rating with no offered or needed exemption.
500-series Citations with MTOW above 12.5k lbs are legacy airframes with legacy cockpit designs certified under Part 25, hence the need for a waiver from two-crew operations - these other airframes are Part 23 or 23 Commuter Category certified with cockpits designed from the scratch for single-pilot operations.
But by all means, please don't stop thinking jumping through the training hoops for a SPW means you're a "better" pilot who gets more stringent checking than anyone flying a modern SP jet...