I am not a lawyer and this answer is my opinion
I couldn't find any legal authorities confirming or denying this, and I assume you speak about NSL-related canaries (those issued by courts to parties work differently).
My apologies for a long answer but it looks necessary to explain some background to answer the question.
First, National Security Letters (information seeking with gag orders) are authorized by 18 U.S. Code § 2709. The law allows the following:
— (A)In general.—
If a certification is issued under subparagraph (B) and notice of the
right to judicial review under subsection (d) is provided, no wire or
electronic communication service provider that receives a request
under subsection (b), or officer, employee, or agent thereof, shall
disclose to any person that the Federal Bureau of Investigation has
sought or obtained access to information or records under this section
The prohibition here is very specific, and it is very easy to formulate the canary the way that it does not disclose this.
However the situation with the individual user private key is different since it falls under communication monitoring, and is covered under 18 U.S. Code § 3123. Its (d)(2) contains the following prohibition:
the person owning or leasing the line or other facility to which the
pen register or a trap and trace device is attached or applied, or who
is obligated by the order to provide assistance to the applicant,
not disclose the existence of the pen register or trap and trace device or the existence of the investigation to the listed
subscriber, or to any other person, unless or until otherwise
ordered by the court.
Here the disclosure prohibition is explicit, and disclosing to the user the existence of a monitoring of their communication by means of compromise of their key would be clearly against the law.
Please also see this article if you're interested in the exact legal details how canaries work.
Update: this article confirms the above reason, explaining:
Such a practice would alert users who become targets of investigations
and cause them to withdraw their business from the company, thereby
jeopardizing legitimate inquiries into individuals who pose actual
threats to national security.
Granular canaries have the greatest potential to compromise
legitimate national security investigations because they could
alert the target of an investigation of the government’s search,
prompting that individual to cease use of the targeted service, and
to attempt to erase his or her information therefrom. Clearly,
the government has a strong interest in preventing this outcome. Thus,
courts are less likely to find that these canaries are legal and are
more apt to uphold a gag order prohibiting their removal.