It's true that a wider price range would capture more potential trade volume, but it's the actual trades that matter. If trades only happen in a much narrower range, then you'd collect a larger proportion of the fees with a narrower price range.

You can think of it like this: imagine it's just one LP other than you and you both supply $1,000 of assets to the pool.

The other LP sets a price range of $90-$110 while you set a range of $80-$120. As long as the price fluctuates between $90-$110, then the other LP will capture more of the fees, since the entire $1,000 they provided in liquidity is within this range. With your wider price range, your $1,000 of liquidity is more thinly spread out - since you'll facilitate less trading volume, you'll earn less fees.

You'll only collect fees once traders use your liquidity, so if the price ranges between $90-$110 and you set a price range wider than this, then some of your liquidity will not be utilized, which means you could've earned more fees setting a narrower range.

Hope that makes sense!