Bhadra is formed by Mercury, and Mercury creates a difficulty the other four members of the set do not. Virgo is both Mercury's own sign and its sign of exaltation, so the two qualifying conditions collapse into one, and Mercury's qualifying signs are Gemini and Virgo rather than the three that Mars, Jupiter, Venus and Saturn each have.
There is a second complication. Mercury is never far from the Sun, at most a little under thirty degrees, so it is frequently combust, and combustion is one of the classical grounds on which a Mahapurusha yoga is held to be weakened. A rule that requires Mercury to be strong is a rule that will often be qualified.
These are not objections to the tradition but features of it, and the classical handbooks discuss both. What the atlas records is the rule as the corpus states it, the conditions the corpus attaches to it, and the fact that the five members of the set are not symmetrical in the way a summary table makes them look. Jyotisha is described here and not offered as guidance, and a reading of any actual chart is the work of a practitioner.
The asymmetry runs further than Mercury. Each of the five planets has its own dignities, its own relation to the Sun and its own dasha length in the Vimshottari scheme, so the five yogas differ in how often they can form, how easily they are undercut and how likely they are to be activated within a life. A table listing them as five equivalent rules conceals all of that, which is the usual cost of tabulating a tradition that reasons case by case.