No.
The switch from requiring 5 close votes to 3 close votes was originally made for StackOverflow (not QCSE) when they had 1000s of questions in the close-vote review queue.
This is not even nearly the case on QCSE, and we have very active close-vote reviewers here.
The vast majority of SE sites still require 5 votes to close a question, and for all other SE sites it was that way for almost 15 years, until the close-vote review queue at SO became extremely un-manageable (but keep in mind, that they get 1000s of questions per day, whereas QCSE currently has 6.6 questions per day.
It is also not true that diamond moderators "can't vote" to close questions. They can vote to close questions, but they choose not to do so because their vote serves as a "hammer" that automatically closes the question and doesn't allow further voting except for re-open voting, which falls under a different process.
A compromise would be for diamond moderators to start using their vote after 2 other votes, rather than waiting for 4 other votes, and then one of your reasons for pursuing this proposal is removed. The other reason that you gave was that we have a "relatively small" number of close-vote reviewers, but I completely disagree with that: We have a relatively large number of close-vote reviewers compared to other sites that have adopted the 3-vote policy. This means that both premises of your proposal are incorrect.
Also, no matter how good or relevant a closed question is, the question can sometimes be deleted by the Roomba within just a few days, which is unfair to the question's asker (and if the question is closed just because it needs some more detail, not because of being off-topic, the asker won't get the chance to edit their question because it will have been deleted). The other consequence of closing a question is that it will not appear in the "unanswered" queue.
Finally, even the author of this proposal says in his first comment on the question, that for the close votes that he sees, the questions are usually getting 5 votes (meaning that we don't need to reduce this requirement to 3, for the majority of the questions), and that only a relatively few questions get stuck at having only 2 or 3 close votes. Keep in mind that not every question with a close vote needs to be closed, and the fact that there's this small number of questions for which there's only 2 or 3 close votes, indicates to me that it's a good thing that we require 5 votes for a question to be closed.
If we do switch to requiring only 3 close votes, I would like the community to first decide on (and agree to) how we would assess whether it was necessary, and to immediately switch back to requiring 5 close votes if it is not found to be necessary.