IIRC, the course progression for pilots is a basic trainer early on, to learn the basics of flying. Think Cessna 152 or 172, though IIRC most militaries use a turboprop and expect the pilots to suck up the extra complications from retractable gear and controllable pitch prop (it's a couple extra things to keep track of, but not all that bad).
Then they go to an advanced trainer, a a Lead In Fighter Trainer (LIFT) like the T38, T45 or T7 for fighter pilots or a King Air for multi engine pilots.
From there they can go to their Operational Conversion Unit for type-specific training.
Little Cessnas (150 and 172) are useful during the first phase of screening potential student pilots to see if they can pick up the basic stick and rudder skills.
While this an initial screening CAN be done in more complex airplanes, it only passes the brightest students. Mid-talented students will struggle with controllable-pitch propellers, retractable landing gear, etc.
The bottom third of potential students will be so overwhelmed by systems that they will not have enough brain-power free to simply fly the airplane.
While this sort of initial screening can be done on turboprop (see Pilatus), I doubt if it can be done on light jets (Canadair Tutor, Cessna T-37).
How and when you screen student pilots is a “big picture” question defined by budgets and training philosophies.
How many candidates are recruited? How many different types of aircraft can your Air Force afford?
How many millions of dollars are in the training budget (e.g. training a CF-18 pilot to operational status costs $6 million).
Side-by-side seating is best for teaching basic and intermediate skills.
Then students who are “pipelined” to fighters need time in tandem-seaters to develop external scanning procedures.
If they are headed for supersonic fighters, they need time in supersonic trainers (T-38 Talon or Red Tail). Many student pilots fail when they let a fast airplane fly ahead of their brains. Those “slower” pilots might still enjoy long careers in lower transport airplanes.
Emergency procedures can be practiced in ground-bound simulators, but hard-core skills (e.g. recovery from upset at low altitude) still need to be practiced in real airplanes.
Two-seat trainers often get forced into ground-attack or intercepting wandering airliners because they are the biggest and fastest airplanes that most Third-World and many Second-World air forces can afford.