According to Ulfric, this is what happened:
When he was a small boy, around 10 years old or so, he was summoned to go train with the Greybeards in order to become one of them. So he went up to High Hrothgar and for around 10 years trained in the way of the Voice. When he was an advlt, the Great War broke out, and he left the Greybeards against their will to go participate in it, etc.
So, from what I take from his story, it actually isn't just so easy to hop up to High Hrothgar and get your training on. Ulfric started as a child and spent a decade learning the Way of the Voice, not something just anyone can do.
Anyhow, I still don't think it's a true need. Torryg ends up in Sovngarde, where you meet him. The gods of Skyrim didn't judge him as badly as Ulfric did, apparently. Elisif says that Torryg respected Ulric.
Ulfric ends up in Sovngarde as well if you kill him before getting to that part of the main quest.
The time-line makes sense, as far as I can see, if Ulfric was about 10 when he began to learn to shout and around 20 when he left for the war. That would put him in his mid-40s right now.
Still not a need to do it that way. Killing your own brothers - brothers who are willing to listen to you and might even side with you - isn't really necessary. He might want to free Skyrim, but his motives there are something else entirely different. He was always vying for the position of high king apparently.
To be fair to Ulfric, he actually goes out of his way to spare people who are fighting against him, especially his brothers and sisters in war. He didn't want to kill Legate Rikke even though she fought against him, and practically begged her to leave so he wouldn't have to do it. He went out of his way to make sure that Balgruuf was spared as well. Ulfric killed Torygg, which is definitely a mark against him character-wise, but other than that he is pretty lenient when it comes to killing others. General Tullius is MUCH more bloodthirsty.