From the linked article:
Other factors, [a White House] lawyer said, were that it would “kill recruitment” for the firms to be publicly associated with representing the polarizing president and jeopardize the firms’ relationships with other clients.
Though I'm not an attorney, my firm "lives and dies" on its reputation more than anything else. Of all the things one might have learned about Trump, one of them most certainly is that the only reputation that may matter to him is his. It's simply not acceptable for consultancies, law advocacies, accountancies, etc. to risk their existing revenue streams and recruitment stance by involving themselves with Trump.
It's simply absurd to do so.
Accordingly, while the cited article presents the factor described above as an "other" one, the risk management assessment principals at law firms surely performed in considering the pros and cons of taking Trump as a client more than likely comprised the controlling reason for why they were unamenable to accepting any actual or potential offer of engagement. Everything else the firms said rung to me (a senior principal in a professional services firm) as nothing more than polite verbiage for saying "no."