Temurah 3b - swearing to the truth

The gemara has what seems to me to be an astonishing הוה אמינא: that the prohibition of misusing Hashem's name - punished by malkus - might include even swearing to the truth. As Rashi says, the verses in Mishpatim might allow you to swear to save money from someone's claim, but you'd still get malkus since you brought yourself to swearing!

The gemara will bring verses to show that swearing to the truth is indeed allowed (ובשמו תשבע). But I don't understand the idea at all. People in Chumash, and Tanach, are constantly swearing to each other. Tzaddikim, too - Avraham to Avimelech is maybe the first. Why can't any of those verses be brought as proof?

The truth is that we say in Aleinu,
כי לך תכרע כל ברך, תשבע כל לשון
It seems that just as it is an honor to Hashem that everyone bows only to him, so too it's a honor to him that we swear in his name.

It would appear that : 1) if there are several Psukim or answers the Gemara can give, then any one is good enough. It is not a Kasha to say why did the Gemara not bring a different one. As Tosafos says, the Gemara brings one answer, although there are others.

Also, a Pasuk about Avraham, who was before Matan Torah, may not be as strong a proof as a pasuk which is in Devarim that seems to clearly state generically that one may swear, and was after Matan Torah. Also, this pasuk is a general statement, not a story, so it is a stronger proof. In the story examples, one might always ask that perhaps they were swearing for some other reason, such as Aseh Docheh Lo Taaseh or some other consideration. So a proof from a pasuk that permits it is stronger than a story.