There is a spec for pool pockets. Whether the spec is tight enough -- both in size and tolerance -- is up for debate, but it does exist. Here it is, directly from the WPA website.
The pocket openings for pool tables are measured between opposing cushion noses where the direction changes into the pocket (from pointed lip to pointed lip). This is called mouth.
Corner Pocket Mouth: between 4.5 [11.43 cm] and 4.625 inches [11.75 cm]
Side Pocket Mouth: between 5 [12.7 cm] and 5.125 inches [13.0175 cm]
*The mouth of the side pocket is traditionally ½ inch [1.27 cm] wider than
the mouth of the corner pocket.
Vertical Pocket Angle (Back Draft): 12 degrees minimum to 15 degrees maximum.
Horizontal Pocket Cut Angle: The angle must be the same on both sides of a pocket entrance. The cut angles of the rubber cushion and its wood backing (rail liner) for both sides of the corner pocket entrance must be 142 degrees (+1). The cut angles of the rubber cushion and its wood backing (rail liner) for both sides of the side pocket entrance must be 104 degrees (+1).
Shelf: The shelf is measured from the center of the imaginary line that goes from one side of the mouth to the other – where the nose of the cushion changes direction – to the vertical cut of the slate pocket cut. Shelf includes bevel.
Corner Pocket Shelf: between 1 [2.54 cm] and 2 ¼ inches [5.715 cm]
Side Pocket Shelf: between 0 and .375 inches [.9525 cm]