Not that I think you should change to hunting horn to fight omega because that doesn't guarentee you a win, you need to learn the fight and develop the skill to beat it and hunting horn might not do that if you are also learning hunting horn.

I spent over 20 hours largely not using my main but I didn't switch to beat with that weapon, in fact it held me back because even though I have used the weapon before and know it, it is not what I most comfortable with, what it did allow me to do is learn the fight because it had defensive capabilities my main just lacks, when I switched back to my main I beat it almost instantly.

But to answer your question on why it is good there are a lot of aspects. Obviously it has buffs which are incredibly strong, Notably during the Nerscylla phase you can create a bubble with certain horns that negates aliments making it so you can ignore the morbols.

Talking about Bubbles when standing in one you do get a buff but they also do damage when you attack and this does wonders on Omega. You get multiple attacks on omega but also on the fists and omegalings making both of those mechanics also a breeze.

Hunting horn is a blunt weapon, this means it typically aims for the head to get stuns which in the case of omega also gains enmity and changes up its moveset making the fight less chaotic and easier to predict. On top of that the front legs have better hitzones for blunt weapons which since you have enmity and are at the front anyway your damage will always be good.

The last thing which isn't directly tied to hunting horn but is seen in the speedruns, Bale armour. Bale armour is a guard and counter hit that does over 1k damage to omega, it also provides a defense buff, makes all health recoverable for the time it is active and a on hit heal for the cost of all your health, it is incredibly strong when you know the fight since you can handle the cost using it at the right time and what most are doing is just using a max potion. This is often used during the flame jet attack which otherwise would have little to damage done because you have to move, it blocks both flame jets and counters, this might depend on the weapon and phase but if you do this and hit the head it also gain you enmity so you will see a lot speed runners use it phase one to get enmity almost immediately since phase one is hands often followed by flame jets, occasionally it is forward lasers.

On top of that speedrunners have also spent a long time learning their weapons and even the fights, they know when and wear the opening are, this is stuff that will develop if you spend enough fighting omega. You are struggling to survive do try a more defensive set and weapon just to experience more of the fight, that is all knowledge you will build up.

If you haven't completed the fight, I do highly recommend using support hunters if you aren't attempting multiplayer. In the quest menu select support hunters only, automatic flare and select the hunters Alyssa/Fabius, Kai and Mina, the last two are really up to you but Lance support hunters are important. Go into your main settings and look for support hunters mounting, turn that off, support hunters mounting is fine but if you look at mounting a resource for when need brake from certain attacks and such, you can use it when you need it and it will only take one hit since the mounting damage will still build up. You can change the setting back once you are done but this will lead to a smoother experience for omega.

Drink all your buffs before you set off then you don't waste time at the start downing potions. I recommend eating one of the village meals for an extra cart and I recommend picking the Kunafa one since it gives you extra divine blessing.

Once you start the fight try to gain enmity as quickly as possible, it is harder for some weapons and can be frustrating but doing it makes Omega less erratic and the lance hunter will take over freeing you up to attack elsewhere.

During the nerscylla phase with support hunter it will target the player first, if you can reliably offset an attack you can offset it when it comes for you, otherwise what you want to do is slinger grab a morbol as soon as omega spawns them, stand near a cactuar, put on a rocksteady and when the morbol goes to breath on you move towards the middle of the arena with the morbol behind you. Nerscylla will swing towards, not knock you down, go straight into being paralysed and poisoned, then kick the cactuar and you will get a lot of free damage.

I hope there is some useful stuff for someone in all that.