The issue of metzitzah on the Sabbath is an old one. The first to twist himself into knots over it was Tiferet Yisrael (Boaz, Sabbath 19), and he indeed reaches a strange conclusion: that on the Sabbath one should suck weakly. Rabbi Kook (Da’at Kohen, sec. 140) wrote a nice responsum. After refuting the questioner’s words that we maintain metzitzah for kabbalistic reasons, arguing that this is not how one analyzes a Talmudic passage and that the plain sense of the Talmud is that it is medical treatment, he goes on at length to explain that we do not rely on doctors in order to be lenient, and when we have a tradition from the Sages that without metzitzah there is danger, we cannot set their words aside—especially since it cannot be empirically proven that metzitzah has no benefit, because who knows how many were harmed and how many died because metzitzah was not done for them. His words are appealing, but twisted and forced (and Tzitz Eliezer, vol. 8 no. 15, followed him in this).
Dr. Halperin’s remarks were said only in order to make sense of the matter, but certainly they do not provide any significant argument to justify metzitzah ab initio had it not been written in the Talmud. I also heard in the name of a well-known urologist that his remarks are nonsense.
I also heard that Dr. Levy from Bayit Vegan had a theory similar to Halperin’s, and presented it before Rabbi Shlomo Zalman Auerbach. Rabbi Shlomo Zalman refuted it on the spot and replied with a question: if a patient came to you with a wound, or even your own small son, would you do “metzitzah” for him?!…
I’ve been very brief. In any case, my feeling is that the matter is not sufficiently clear, although when it comes to actually performing metzitzah on the Sabbath I’m not worried about going to hell…

That is exactly what I said. I’ll just note that I do not agree with Rabbi Abraham Isaac Kook’s view that one does not rely on doctors in order to be lenient:
First, this is also being stringent (in the laws of the Sabbath) and not only being lenient (in the laws of circumcision).
Second, why should we not rely on them, just as we place our lives in their hands and do not use the medical methods of the Sages? Is that too a stringency and not a leniency? After all, we are risking our lives.
And third, why assume that the Sages had any special knowledge such that anyone who departs from them bears the burden of proof? Most simply, they went by the knowledge available in their time. So it is absurd to say that we should not go by the knowledge of our own day, which is certainly broader, more systematic, and more authoritative than what existed then. Why were they allowed to go by their medical knowledge and permit desecration of the Sabbath—that is, to be stringent on the basis of the shaky medical knowledge of their time—while we are forbidden to go by the more reliable medical knowledge that we have? Of course there can always be mistakes, but the chance of medical error among the Sages was far greater, and they were not concerned about it.

As is well known, a whole group of later authorities—Maharam Schick, Mahari Assad, Arukh LaNer, and many others—understood that in metzitzah, besides the issue of danger, there is also an integral component of the commandment of circumcision, and that it is a law given to Moses at Sinai. (Some inferred this from the words of medieval authorities, although one can argue with their inference.) And the words of Or HaChaim are well known: “And God commanded that this blood be sucked out because it too is a form of foreskin.”

(But apparently from the Talmudic passage in Sabbath it sounds as though there is indeed some value in metzitzah even aside from the reason of danger, yet on the other hand it seems that were it not for the reason of danger they would not do metzitzah on the Sabbath, nor would they remove a circumciser who does not perform metzitzah.)

In any case, in practice it would seem fairly clear that there is no danger on the level of danger to life in not doing metzitzah, since millions of people are circumcised around the world every year without metzitzah and the great majority of them remain alive. (And even the few who die, it can usually be shown that they died because the circumcision was performed incorrectly and not because metzitzah was omitted.)
Perhaps one could say, with some difficulty, that even if this does not rise to the level of danger to life, there is still a very remote concern of danger, and that is enough to remove a circumciser who does not perform metzitzah; and that this remote danger is enough to define the act as an accompanying part of circumcision, and since circumcision was permitted on the Sabbath, all of its components were likewise permitted (and not because of danger to life)—but this is forced.

Apparently, when we perform metzitzah on the Sabbath, even though there is no concern at the level of danger to life, we are concerned for the view that this is part of the commandment of circumcision, even if that is a bit difficult in light of the Talmud. Otherwise, it is hard to explain our practice.