Elephants are always a funny kind of weapon
Having a big weapon on your side is a terrible advantage. Elephants are a good historical example: while they don't deal a lot of damage per se, they are terrible for enemy morale. You can only have a few, and each of them won't deal a lot of damage. But if you are on the other side, that's another topic.
Gosh, an elephant charging me! Ok, so if we all keep the formation, the elephant will crush on our spear formation. Sure, there will be casualties, but we will win. The only thing we had to do is keep our formation. Hey, what is Joe doing? he can't escape the battle, can he? Whatever, he was a coward. We can keep formation without him. But, wait, Jack is also fleeing! He was the best of us. If even he thinks we are lost... But we need to keep the formation! Oh, no, some others are also running. The formation just broke up, the odds are very bad for me. Yep, better run for my life.
Even if the elephant wouldn't do that much damage, it crushes the enemy formation, and you can now deal much more damage.
Why on earth wouldn't you want such a weapon?
Sure, the enemy also have a huge weapon, but that won't ensure that the foot soldiers will keep the formation.
And it's because she doesn't have dragons that she wants a similar, smaller armed animal that can afraid the enemy.
So that we don't expect elephants
Golden company is well-known for their elephants. Harry Strickland is proud of them, and as it's the final season, we expect massive battles. This scene is also a way for showrunners to tell the spectators to don't expect any elephant. Sorry, all CGI budget was burned on dragons.