Ok let's run down some CDs of other top laners:
Aatrox: 100s
Cho'Gath: 60s - He NEEDS to be able to build and rebuild stacks quickly)
Darius: 100s - I dislike comparing Darius to Garen to be honest because their play patterns are quite different really. He has no real way to mitigate damage and only has one other spell that does noticeable damage. On top of that he must be MUCH more lenient with his spell usage because of his mana puddle.
Dr. Mundo: 75s - Like Cho, Mundo's ult is needed for him to be functional
Fiora: 130s - Probably the best ult to compare to Garen's as they share a lot of the same play patterns despite her being focused more on offense and aa's rather than Garen being focused on defense and spells. They even have similar passives. While she's still mana-restrained, it's not nearly as much as Darius. She also doesn't necessarily need her ult to deal significant damage.
Gangplank: 120s - Another one who absolutely doesn't need his ult to make plays.
Irelia: 60s - The damage from Transcendent Blades is meh at best without items (Sheen procs specifically). Most of the time, Irel's just using it to heal, push a wave, or output damage into a fight she can't dive into.
Kennen: 120s - Needed for teamfights, but not for 1v1 or 2v2 encounters.
Malph: 130s - See Kennen
Nasus: 120s - See Kennen. NOBODY that's ever played as Nasus nor against a good one thinks his ult's damage is what makes him threatening.
Olaf: 120s - See Kennen
Panth: 150s - See Kennen
Poppy: 140s - See Kennen
Renek: 120s - See Kennen/Nasus
Rengar: 140s - See Kennen
Riven: 110s - Another one that's good to compare to Garen, but Blade of the Exile has multiple use cases aside from the execute (you can use the AD amp to increase the strength of your shield if you're about to take a heavy burst of damage). Being honest, I'm afraid adding things like CC to Demacian Justice to increase it's use cases would make him more like her in a weird way.
Rumble: 105s - See Kennen. Also skillshots deserve to have lower CDs because there's a chance that they do nothing for you.
Shen: 200s - See Kennen
Singed: 100s - See Kennen
Tryndamere: 110s - Comparing him to Garen wouldn't so much be used to give Demacian Justice a lower CD as much as give Undying Rage a higher CD.
Vlad: 150s - See Kennen/Nasus
Wukong: 120s - See Kennen
Xin: 120s - imo Crescent Sweep has never been in a good place. It's an ult that does damage based on current HP, so it should be used when they're as full as possible, but I still constantly see it used as a finisher. When used for its CC, that's perfectly understandable, though.
Yorick: 120s - Ugh. I don't even want to talk about the mess that is Yorick.
Conclusion: Yes Garen's ult could possibly use a CD buff at lvl 1, but there would have to be some tradeoffs because there is no situation where you can 1v1 a lvl 6 Garen when you're low. With Darius, he can be oom. Fiora's ult doesn't do inordinate dmg in itself against one target and she can be oom. Riven and Rumble can miss. Garen doesn't have any of these concerns. There's no counterplay involved with it and that's why his CD has to be so high.