"Aerith is weak in battle" they said.

[Carl the Llama]

She is momentarily a bit more powerful than the rest. It's a temporary anomaly, not the standard mode of operation. Isn't the parasol also the item you get from the rail shooter? Terrible controls. Never want to do that again.

Of course she can be a physical attacker. Anyone can be. That doesn't mean she isn't weak. Weak is a relative term, and she is weak compared to many others.

Actually its pretty much the standard if you know the ins and outs of the game:

Striking Staff: stolen @ the train graveyard (Aerith strongest)
Hardedge: stolen @ Shinra Tower (second)
Atomic Scissors: stolen @ World map (third)
Grand Glove: stolen @ Mythril Mines (weakest)

From this point she become the weakest again until you get to the Golden Saucer for the first time so... Gongaga > Cosmo Canyon > Nibelheim > Rocket Town > (optional) Wutai (Yuffie Superball) > Golden Saucer > Temple of the Ancients.

This is hardly a temporary anomaly... Also while you may not like the rail shooter, others may have different opinions and like a bit of a challenge (like myself).