This is an excellent question. It is true that certain CAs, like Symantec, will not issue DV certificates to financial institutions. I know that the CA/B Forum Baseline Requirements contains rules related to "high risk certificate requests".
However, I believe that there is nothing preventing automated assessment of so called high-risk certificates.
From the BRs (bold added for emphasis), a definition:
"High Risk Certificate Request: A Request that the CA flags for additional scrutiny by reference to internal
criteria and databases maintained by the CA, which may include names at higher risk for phishing or other fraudulent usage, names contained in previously rejected certificate requests or revoked Certificates, names listed on the Miller Smiles phishing list or the Google Safe Browsing list, or names that the CA identifies using its own risk‐mitigation criteria."
Later, in section 4.2.1, the BRs state:
"The CA SHALL develop, maintain, and implement documented procedures that identify and require additional verification activity for High Risk Certificate Requests prior to the Certificate’s approval, as reasonably necessary to ensure that such requests are properly verified under these Requirements."
As we can see, these are suitably vague rules. Please note that the term "SHALL" is used as defined in RFC 2119 which establishes the word is synonymous to "MUST".
Let's Encrypt has previously stated they plan to have a few procedures that will would seem to fit the bill of "additional verification activity". They have stated that validation challenges will be performed through multiple network paths to help prevent network impersonation and spoofing (though it seems this may not be ready for launch). They have also described a method called "Proof of Possession" (I believe thats the name anyways...) which will be used when a Let's Encrypt certificate is requested for a domain which already has a certificate through another CA (including Let's Encrypt). This method will require a challenge that will require the signature of the existing certificate's private key.
That being said, EV certificates would still provide additional security which financial institutions should probably take advantage of. The cost of an EV certificate (~$150/year) should not be a problem for them, and the validation should be easy given that they usually have things in order due to other compliance requirements.
Symantec's refusal to offer DVs to financial institutions seems to be a policy they have a adopted which is more strict than the BRs require. This is likely to protect their image and reputation. As far as I know, most CAs dont do this - Comodo for instance does not have this restriction AFAIK.
Let's Encrypt should adopt a list that rejects common phising targets, such as purposeful mispellings of notable brands such as "gmall.com" or "paaypal.com"