Since when does a manga character use their best form of fighting as the first choice?
Kaku engaged Zoro with swordplay first, which is just as good as his Rokushiki.
Zoro pulled out all three sword to start fighting people more than once. It's not as uncommon as you think.
Also, it's not about using it the first time, it's the fact that it's the only thing he's used EVERY time, including against top tier fighters like Whitebeard and Akainu.
Luffy uses a base attack or G2 or even G3 to gauge his opponent's strength before attacking with G4.
Gear 2, 3, and 4 are not fighting styles. They are enhancers. Luffy's fighting style remains the same regardless of which Gear he is using: Punch, kick, scratch, and claw. He's a brawler, and regardless of which Gear he is using, he fights the same way every time.
Shanks pulling out his sword first doesn't mean it's not his primary fighting style. It just means that, like Luffy, he has ways to upgrade that style when the battle gets more serious and he's done gauging. With Luffy, it's the Gears, and with Shanks, it's more than likely Haki. Either way, it's still just one fighting style being upgraded, not switching to a new style of combat.
Good writing on Oda's behalf is having a man with one arm use his sword to block attacks from fire or magma or sharp objects.. like why would I use my one and only arm, when I have a sword on my waist?
Except Akainu was the only time Shanks pulled out his sword as a response to what another person was doing. He drew his sword BEFORE Ace did anything to attack. He pulled out his sword BEFORE Whitebeard did anything to attack. He pulled out his sword BEFORE any of the Marines took on his challenge. So it's not like Shanks is going "Hmm a sword is the best thing to use here," using a sword is simply his primary choice. It's not a situation by situation basis, it's a choice he makes every time.
The whole point went over your head I see..
WhiteBeard vs Mihawk
WB can only use his bisento.
Or
WB can use his bisento, DF, fist, anything he wants.
How would WB's other methods be only equal to his Bisento at best???
This has absolutely nothing to do with Shanks vs Mihawk because Whitebeard isn't a swordsman, and this doesn't match your point.
Another reason this fails is because WB's primary style of fighting is releasing Quakes towards his enemies. He does so by infusing his Quakes into his fists or Bisento. He barely ever punches normally or uses his Bisento to actually cut a person.
A person's primary style of fighting is going to be what they are capable of delivering their max output with. Meaning that if Shanks has a martial art, if his primary style of fighting is his sword, his martial art won't be as good as his swordplay because the latter is PRIMARY. It's what he does and uses the most. Just like Sanji's kicks are his primary fighting style, so they're better than his ability to use knives/swords.
I know what point you're trying to make, and it's wrong.