[Aegon the Unworthy]

"Relax everybody, Im here" Jack Burton-Big Trouble in Little China

Actually youre kinda missing the point in sea battles there LotM. The limiting factor in sea battles is ships not manpower. The limiting factor in those ships is your ability to repair and replace them.

With the Tyrells fleet on the east coast, their ability to sustain and reinforce that fleet were undefended on the west coast. By striking at the Tyrells theyve shortened the duration the Tyrells can expect to maintain full operability on the ocean, in fact they are now living off of former Tyrell land. Which in a sense acts as a form of "force multiplication". Thats a fancy term for essentially making the enemy weak at the same time you make yerself strong.

So if they attack the east coast, not only will the Tyrells be able to counter relatively quickly, but the possible gains out of such a raid will be less (war-torn Lannister lands vs the prospering untouched Arbor) and likely defended better.

Dont get me wrong, living off the Tyrells is a bold move, but now you force them to decide if they want to attack the well-defended but resource poor Greyjoy islands and allow the Greyjoys to resupply themselves from the Tyrells own larders or retake their own islands in a relatively empty gesture which would likely destroy those strongholds in the process.

If the Tyrells fleet is so large as to be able to destroy them quickly, Euron has no chance in the first place. If not a War of attrition could take place where the Greyjoys are able to replace their ships and supplies quicker than the Tyrells can. Thats a good way to make the war winnable.