Chazal (Brachos 5) darshen the pasuk, "Rigzu v'al techet'u" (Tehillim 4:5) to mean that a person should "yargiz"=incite his yetzer tov to fight his yetzer ha'ra. If that's what the pasuk means (as opposed to "rigzu" meaning to fear G-d, as Rashi/Metzudos explain al pi peshuto), then isn't the pasuk being repetitive? "Rigzu" = fight against your yetzer ha'ra so as to not sin; "al techet'u" = don't sin. Same thing?
Chazal continue their advice in that same sugya (Brachos 5) and tell us that if you are challenged by the yetzer ha'ra, the first response should be to run to the beis medrash; if that doesn't work, read kri'as shema; finally, if all else fails, think about the day of death. (Parenthetically, the Targum Yonasan at the end of our parsha comments on the phrase "haima bochim pesach ohel mo'ed," which describes the reaction of the onlookers to Zimri's brazen challenge to Moshe, that the people were crying and reading kri'as shema. Why does the Targum stick kri'as shema into the mix here? I can't recall where I saw it (my wife's cousin in his sefer Na'ar Yonasan quotes a similar idea sefer from the Nitaei Chemed, a talmid of the Mahari"l Diskin), but I remember seeing that the Targum is based on this gemara. The yetzer ha'ra was running rampant, and so the people followed the steps Chazal prescribed to stop it. Step #1 is come to the beis medrash, which is what happened when Zimri approached Moshe. That step failed since Moshe forgot the halacha in this case. The people then moved on to step #2 and began reading shema.) If step #3, remembering the yom ha'misa, works when all else fails, why not just cut to the chase and always use that strategy? Why bother with steps #1 and #2?
Earlier this R' Zev Leff was visiting the US and he mentioned this question in a shiur. He answered that Chazal did not want a person to walk around thinking about death all the time. That's not a healthy attitude. It's a last resort when nothing else works, but not something to make into the norm. My wife's grandfather, R' Dov Yehudah Shochet, offered a different answer. Were the goal simply to stop the yetzer ha'ra in its tracks, then maybe indeed we could cut to the chase and go directly to step #3. But the Torah doesn't just want us to not act on our urges and not sin. The Torah wants us to be people who don't feel those urges to begin with. The purpose of coming to the beis medrash (step #2) or concentrating on the ideas in kri'as shema (step #2) is exactly that -- to shape out attitude and character so that we become people who not only don't do wrong, but also are not tempted to do wrong.
These are the two steps David haMelech is speaking of in Tehillim: "Rigzu" - engage in battle with the yetzer ha'ra so that you don't even have the desire to do that which is wrong or improper; if that fails and you do feel temptation, then at least, "al techet'u," don't succumb and act upon it.
Turing to out parsha, Bilam was not satisfied with Hashem's response telling him not to go to help Balak, so he asked yet again for permission to go. Chazal tell us that chutzpah works even when it comes to getting things from Heaven and "b'derech she'adam rotzeh lei'lech molichin oso," and so Hashem eventually said yes. So why was Hashem so angry at Bilam for going? He asked and got permission?!
My wife's grandfather suggested that it's not the going which Bilam was at fault for - for that he had permission. There was no violation of "al techet'u." What Bilam was at fault for was the desire to go. Even though he knew it was wrong, Bilam could not curb his desire to go and so he nagged and asked until he got the answer he wanted. It's the idea of "rigzu," shaping his attitude and desire to be in consort with ratzon Hashem, not in constant battle with it, which Bilam failed to live up to.