Question

Why are temples devoted to Brahma so rare?

Answer

"I am of course familiar with the standard mythological justification."
The story you mention isn't actually the standard justification for why Brahma isn't worshiped. But since you were wondering, the justification you give is from the Vidyeshwara Samhita of the Shiva Purana. In this account, Brahma and Vishnu argue about who is superior until this argument turns into a battle. The battle threatens to destroy the three worlds, so the devas (gods) go to Shiva for help. To stop the conflict, Shiva turns into a pillar of fire that seems to go forever in both directions. Both Brahma and Shiva are curious about what it is, so Brahma turns into a swan to go to the top, and Vishnu turns into a boar to go to the bottom. Both are unsuccessful, but Brahma lies that he went to the top, presenting a Ketaki flower that arose from the middle of the pillar and claiming it's from the top. Vishnu concedes defeat, but then Shiva appears, Vishnu touches Shiva's feet and as a result Shiva grants Vishnu the privilege to be worshiped as an equal to Shiva. Shiva then creates the demon Kala Bhairava to cut off Brahma's fifth head, but Vishnu persuades Shiva to take mercy on Brahma, so Shiva instead curses Brahma that he can't be worshiped in temples.

The version of the story given in the Shiva Purana is likely a later interpolation, because it differs from more common versions in a variety of ways:

  • In most versions the argument between Brahma and Vishnu does not come to blows;
  • In most versions Shiva explicitly offers help to the two gods by proposing a race;
  • In some versions Shiva just turns really tall without turning into fire;
  • In most versions the Ketaki flower falls from Devaloka instead of the middle of the pillar;
  • In Vaishnava versions Vishnu just touches Shiva's feet to tickle him so he'll bend down and Vishnu can touch his head and win.

But the most important difference for our purposes is that in most versions, Kala Bhairava actually does cut off Brahma's fifth head rather than showing mercy, and Shiva does not actually put any curse on Brahma. (In fact in these versions the opposite happens: Brahma puts a curse on Kala Bhairava that he'll be a vagabond.)

In any case, the more common justification for why Brahma isn't worshiped actually comes from another story, one recounted in many places, for instance in this excerpt from the Uttara Kanda of the Padma Purana. (I described it earlier in this answer.) A group of sages were conducting a yagna (ritual) on the banks of the Saraswati river, when they started to wonder (on the prompting of Narada) which god to dedicate the ritual to. So they sent sage Bhrigu (famous for his short temper) to test which god out of Brahma, Vishnu, and Shiva was most worthy. When he went to see Brahma, he put his hands together to salute Brahma. But Brahma was too proud to honor Brighu in any way, so outraged by this disrespect Brighu cursed Brahma that he would no longer be allowed to be worshiped. (By the way, if you're interested Vishnu was the one who ultimately won the test, although it had major ramifications that led to the story of Tirupati Balaji, AKA Venkateshwara.)

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