Parsha Balak - Why was the Parsha named for Balak when Bilaam seems to be the central figure?

sources for pesukim below the text

Balak is appointed king of Moab and sees what the Jews just did to Emor. He enlists Bilaam to curse the Jews. Balak says to Bilaam: "כִּ֣י יָדַ֗עְתִּי אֵ֤ת אֲשֶׁר־תְּבָרֵךְ֙ מְבֹרָ֔ךְ וַאֲשֶׁ֥ר תָּאֹ֖ר יוּאָֽר׃"

Bilaam consults with HaShem, who tells him not to go. Bilaam persists, and HaShem tells Bilaam that if he goes, Bilaam will have to do whatever HaShem commands him to do. Bilaam goes to Balak, and they make 7 sacrifices to HaShem. Bilaam tries to curse the Jews 3 times, and each time he ends up giving the Jews a blessing.

Why did Balak hire Bilaam and pay him enormous amounts of money to curse the Jews?

In the Gemara Brachot, hazal explain that on each day, for just a moment, HaShem gets angry and makes a "hard judgment" (i.e., seemingly one that does not take into account His rachamim). And a “moment” - a rega - is only as long as it takes to say rega. This moment of HaShem’s anger is so powerful that hazal tell us that when Moshe was going to pray to HaShem to abate the punishment for the cheit ha'egel, HaShem told Moshe to wait until the rega of anger passed before praying on the Jews’ behalf. We also know that this rega of anger was so strong that Moshe says that even the merit of all 3 avot is not enough to overcome this rega of anger.

Bilaam was "special" because he knew when HaShem’s rega of anger came each day. This gave him a unique ability to pray to HaShem during the rega in order that HaShem should judge a person without the balancing effects of rachamim. Balak wanted to harness that ability against the Jews.

There is another side to Bilaam’s power of knowing HaShem’s rega of anger: Bilaam could avoid davening during the rega in order to ensure that HaShem's judgment was done with rachamim. In fact, the pasuk explicitly tells us that Balak knew this: “asher tevarech, mevurach” “whoever you [Bilaam], bless, is blessed.”

So, instead of asking to curse the Jews, Balak could have asked Bilaam to spend 23 hours, 59 minutes and 59 seconds of the day requesting blessings for Moab (i.e., throughout the day, but avoiding the rega of anger), so that Moab would be victorious!

Sforno asks why Balak didn't ask for the blessings instead? He answers that Bilaam didn’t actually have the power to bless. Instead, Balak was saying that whoever Bilaam blesses is already blessed (i.e., already deserving of HaShem's blessing). Bilaam’s blessing could not have a positive effect. I have 4 issues with Sforno’s understanding:

1. The Midrash Tanchuma and Rashi tell us that Balak knew about Bilaam because he blessed Sihon in their war against Moab and Sihon eventually won. From this we see that Balak believed that Bilaam did have the power to positively affect people by praying that they should be blessed. ​​​​​​​
2. Moab had merit that could have been the basis for a blessing. Moab were descendants of Lot; and Ruth and Dovid HaMelech were descendants of Balak / Moab. So even according to Sforno, Bilaam should have been able to bless Moab.
3. The Gemara tells us that “you should not take the blessing of an ordinary person lightly.” Bilaam was at least an ordinary man. Perhaps even more since he was the greatest navi for the goyim.
4. The Parsha tells us that Bilaam told Balak: "מָ֣ה אֶקֹּ֔ב לֹ֥א קַבֹּ֖ה אֵ֑ל וּמָ֣ה אֶזְעֹ֔ם לֹ֥א זָעַ֖ם ה׳׃", so Bilaam understood his power to curse was exactly the same as Sforno understands his power to bless – that it is dependent on the person who is being cursed or blessed.

I’d like to suggest that perhaps there is another explanation that explains what Balak was asking from Bilaam. Balak understood that Bilaam had the power to bless Moab, but to him, it seemed more of a certainty to rely on the negatives of bnai Yisrael (because, who doesn't have a sin that would be worthy of HaShem's wrath if He didn't judge with rachamim?) than the good qualities of Moab. In fact, it was easier to assume that the bnai Yisrael had done something worth cursing than to do the teshuva necessary to be worthy of brachot.

Balak's plans were foiled because he did not anticipate that HaShem would make the bnai Yisrael immune to curses. HaShem says “You cannot curse [the Jewish people], for they are blessed.” And Bilaam only had the power to curse those who are deserving of a curse; he could not curse those who were blessed.