Is there a reason Aave gives you an aToken in exchange for lending to the LP?

Because they are just ERC20 tokens they can easily be integrated to other protocols and various apps.

-You can easily transfer them to another address using your web3 wallet.

-Portfolio trackers can effortlessly intergrate them.

-Other protocols can allow you to use them as collateral without too much work.

aTokens are a way to tokenize the deposit or borrows of users. By tokenizing this, it allows for integrations to be built on top of Aave e.g. supplying liquidity directly to the aTokens like Balancer and Curve do with their Aave stable pools.

It is not much less gas efficient due the extra erc20 layer, but this allows others to build on top of Aave;