The first limitation is that the president cannot revoke a visa, and cannot literally compel the Secretary of State to do so. The Sec'y must decide whether to comply with the order. The second limitation is that as that paragraph states,
There shall be no means of judicial review (including review pursuant
to section 2241 of title 28 or any other habeas corpus provision, and
sections 1361 and 1651 of such title) of a revocation under this
subsection, except in the context of a removal proceeding if such
revocation provides the sole ground for removal under section
1227(a)(1)(B) of this title.
In such case, the courts may review whether the revocation is legal,that is is consistent with the totality of applicable law. Apart from being consistent with the wording of the statute passed by Congress, this includes consistency with constitutional requirements, federal regulation, and law as constructed by judicial interpretation. Revocation is addressed regulatorily at 22 CFR § 41.122. There are various classes that are statutorily and/or constitutionally protected, for example race and religion are not allowed classes of immigrants subject to visa-revocation.
In Wong v. DOS, 789 F.2d 1380, plaintiff was granted a visa which was later revoked on illegal grounds, that dependent were not physically present within the consular district, which is not a permissible grounds under 22 CFR 41.134(a). This relates to 8 USC 1182, which enumerates lawful reasons for deeming an alien inadmissible (health, criminality, government officials committing particularly severe violations of religious freedom, etc.). In this case, a consular officer revoked the visa and the court found that the revocation was illegal under existing regulations. On the other hand, in the case
Noh v. INS, 248 F.3d 938, plaintiff's visa was revoked by the Deputy Assistant Secretary for Visa Services (DOS). The court found that the Deputy Assistant Sec'y was not acting as a consular officer so was not subject to those rules. In a lower court review, the Board of Immigration Appeals refused to hear the appeal because
Our jurisdiction does not include review of a State Department
official's decision regarding the issuance or revocation of visas,
which is within the domain of the Department of State
The federal appeals court agrees. Plaintiff also claims that revocation was based on "no facially legitimate reason whatsoever". The court did not reach the question of whether a literally arbitrary basis would subject the decision to judicial review, since "the Secretary offered a facially legitimate and bona fide reason for revoking Noh's visa", namely that it had been obtained illegally. This follows from the holding of Kleindienst v. Mandel, 408 U.S. 753 that
In the exercise of Congress' plenary power to exclude aliens or
prescribe the conditions for their entry into this country, Congress
in § 212(a)(28) of the Act has delegated conditional exercise of this
power to the Executive Branch. When, as in this case, the Attorney
General decides for a legitimate and bona fide reason not to waive the
statutory exclusion of an alien, courts will not look behind his
decision or weigh it against the First Amendment interests of those
who would personally communicate with the alien.
where again the decision was based on a lawful grounds for exclusion.
This decision confirms that Congress has delegated powers to the executive branch (Congress can also undo or limit that delegation, if it decides). While the cases can be distinguished in terms of whether the action is a refusal to issue vs. a revocation of a visa, nothing in the statutes or case law suggests that such a difference would result in more stringent guidelines for revocation.
There is no case law that addresses the situation where the Sec'y of State or person to whom power has been delegated provides no grounds whatsoever.
The question of "Congressional intent" would not underlie a successful appeal. On occasion, the courts make decisions based on findings of "Congressional intent", but only in case the wording of a law is unclear and the courts have to decide what the words mean. In this case, there is no unclarity in what Congress said, and the courts do not usurp the power of Congress to pass constitutionally-valid laws.