Mr. Cessna, and Mr. Piper (among other certified airplane builders) built aircraft at the time which conformed to:
Sec. 23.807
Emergency exits.
(a)
Number and location. Emergency exits must be located to allow escape without crowding in any probable crash attitude. The airplane must have at least the following emergency exits:
(1) For an airplane with a seating capacity of more than five occupants, but less than 16, at least one emergency exit on the opposite side of the cabin from the main door specified in Sec. 23.783.
(2) For an airplane with a seating capacity of more than 15 occupants, the emergency exit specified in subparagraph (1) of this paragraph, and an emergency exit in the top or side of the cabin for each seven occupants, or fraction thereof, above 15. However, no more than four exits are required if their arrangement and size allow quick evacuation of each occupant.
(3) If the pilot compartment is separated from the cabin by a door that is likely to block the pilot's escape in a minor crash, there must be an exit in the pilot's compartment. The number of exits required by subparagraphs (1) and (2) of this paragraph must then be separately determined for the passenger compartment, using the seating capacity of that compartment.
(b)
Type and operation. Emergency exits must be movable windows, panels, or external doors, that provide a clear and unobstructed opening large enough to admit a 19-by-26-inch ellipse. In addition, each emergency exit must--
(1) Be readily accessible, requiring no exceptional agility to be used in emergencies;
(2) Have a method of opening that is simple and obvious;
(3) Be arranged and marked for easy location and operation, even in darkness;
(4) Have reasonable provisions against jamming by fuselage deformation; and
(5) In the case of acrobatic category airplanes, allow each occupant to bail out quickly with parachutes at any speed between
and VD.
(c)
Tests. The proper functioning of each emergency exit must be shown by tests.
Note that the current version of this standard is much more demanding.
So, yes, emergency exits are required for all certified aircraft, rather than just transport category. I don't know the Epic, though if it is not a certified design, it has not demonstrated compliance to the design requirements, so its required characteristics are generally those accepted by the purchaser, who best inform themselves.
The C206 is an example of a "challenged" design WRT exits: The P206 was ok, two front doors like a 182, and a third left side exit at the back, which met the requirements. Once the U206 was introduced, the absence of the right front exit became a problem, as the aft clamshell doors were imperfect as emergency exits, if their use was required with the flaps extended. Workarounds were developed over the years. In Canada, the U206H (certified to a newer standard) was limited to being a five place aircraft, as compliance could not be demonstrated as a six place, again, clamshell door operation. Again, there may be workarounds, but this was a hot topic at the Canadian introduction of the U206H.
§ 91.319 Aircraft having experimental certificates: Operating limitations.
(a) No person may operate an aircraft that has an experimental certificate -
(1) For other than the purpose for which the certificate was issued; or
(2) Carrying persons or property for compensation or hire.
Is because the "Part 91" side of the FAA knows that non certified aircraft have not followed the "Part 23/2/27/29" certification route, and their characteristics are unproven.
Even the FAA recognizes that the full Part 23 certification path is very burdensome, and are working to streamline it for some aircraft. But the notion that an "experimental" aircraft can replace a certified one operationally is a stretch.