Why aren’t multiengine general-aviation aircraft required to be capable of sustained single-engine flight?
It is legal to operate a light twin with anemic or nonexistent
single-engine climb performance.

No, and technically it would not be certifiable as airworthy as per § 23.67 Climb: One engine inoperative. Aircraft that were certified at a different point in history may subscribe to different regulations.

(a) For normal, utility, and acrobatic category reciprocating engine-powered airplanes of 6,000 pounds or less maximum weight, the following apply:
(1) Except for those airplanes that meet the requirements prescribed in § 23.562(d), each airplane with a VSO of more than 61 knots must be able to maintain a steady climb gradient of at least 1.5 percent at a pressure altitude of 5,000 feet with the -
(i) Critical engine inoperative and its propeller in the minimum drag position;
(ii) Remaining engine(s) at not more than maximum continuous power;
(iii) Landing gear retracted;
(iv) Wing flaps retracted; and
(v) Climb speed not less than 1.2 VS1.

In other words if you can get to ~5000 Ft. you need to be able to maintain a nominal climb in a light twin.
The regulation for aircraft over 6000 lbs. is similar as well depending on where you draw the line for &quot;light&quot;. There is also more information on how the testing occurs in this AC.