The regulation is the floor, not the ceiling. Two practical forces shape real high-performance and complex operations: insurance and personal currency.
Most owners and flight schools carry insurance with an open-pilot warranty that specifies minimums beyond the FARs — for example, total time, retractable-gear time, time in make and model, and a completed checkout with a named instructor or within the last 12 months. A pilot can be perfectly legal under 61.31 yet uninsured to fly the airplane. Always confirm you meet the policy's named-pilot or open-pilot terms before acting as PIC.
The one-time endorsement does not relieve you of the duty under 91.103 to be familiar with all available information for the flight, including the airplane's performance and limitations. Moving from a fixed-gear Cessna to a Bonanza means new gear logic, a different fuel system, and faster speeds — a focused transition checkout protects you even though no new endorsement is legally required.
A high-performance or complex airplane is less forgiving of rust. Gear, prop, and cowl-flap management are perishable skills. Many pilots set a personal minimum — a flight with an instructor after any long layoff, or a recurring annual checkout — well above the legal minimums of recency (the 90-day passenger-carrying currency of 61.57 still applies).
If your high-performance airplane is also pressurized, separate training under 61.31(g) for pressurized aircraft capable of operating above 25,000 feet MSL may apply. That is a distinct endorsement from (e) and (f).