It is only RECOMMENDED in RFC7208:
2.3. The "HELO" Identity
It is RECOMMENDED that SPF verifiers not only check the "MAIL FROM"
identity but also separately check the "HELO" identity by applying
the check_host() function (Section 4) to the "HELO" identity as the
. Checking "HELO" promotes consistency of results and can
reduce DNS resource usage. If a conclusive determination about the
message can be made based on a check of "HELO", then the use of DNS
resources to process the typically more complex "MAIL FROM" can be
avoided. Additionally, since SPF records published for "HELO"
identities refer to a single host, when available, they are a very
reliable source of host authorization status. Checking "HELO" before
"MAIL FROM" is the RECOMMENDED sequence if both are checked.
Note that requirements for the domain presented in the EHLO or HELO
command are not always clear to the sending party, and SPF verifiers
have to be prepared for the identity to be an IP address literal (see
[RFC5321], Section 4.1.3) or simply be malformed. This SPF check can
only be performed when the "HELO" string is a valid, multi-label
domain name.
And you likely identified the documented problems as they relate to the standard, with an easily readable explanation from Explained from First Principles:
HELO identity
In order to prevent mail loops, no MAIL FROM address is provided in automatic responses. In such circumstances, the address postmaster@ followed by the domain from the HELO/EHLO command is used for SPF evaluation. The HELO identity can also be verified separately by evaluating the SPF record of the HELO/EHLO domain. Mailbox providers would have to configure SPF records for each of their outgoing mail servers. As far as I can tell, this is rarely done in practice. I found SPF records only for the outgoing mail servers of Outlook.com. Unless you run your mail servers yourself, this aspect of SPF is nothing to worry about.
However, there might be "undocumented" reasons, such as proof of work on the receiving server. As while you are, as you stated, free to do with your server as you desire, so are the admins of the receiving servers free to do with your messages as they desire, and how many spam messages have issues related to HELO, and maybe just send those not strictly following the standard to the spam folder, just to be safe.
So perhaps the HELO checks are good to show the admin on the other side you can follow the standards, even including their "spirit".