Why does the FAA require special authorization to act as PIC in the North American T-28 Trojan?
As the T-28 is a vintage military surplus aircraft it is normally certificated in the Experimental-Exhibition category. For most aircraft in this category, there is no type rating in the traditional sense. For years, the FAA managed these aircraft and pilot qualifications for them on a case-by-case basis. Approval to fly them was (and for some vintage aircraft still is) granted by a Letter of Authorization (LOA).
About 15-20 years ago, in an effort to reduce the regulatory burden on both the FAA and pilots they moved to a process that more closely aligns with type ratings. It is managed under the Vintage &amp; Experimental Aircraft Program.
The stated coverage of the program is:

This program standardizes pilot certification in the following U.S.
aircraft:

Vintage Type Certificated aircraft which require a type rating
Experimental turbine-powered aircraft
Experimental aircraft with a maximum gross weight in excess of 12,500 pounds, or
Experimental piston powered aircraft with an engine over 800 HP and a Vne (never exceed speed) greater than 250 knots


The T-28 falls under the last bullet as it has more than 800 hp.