Aggregation of signatures leads to smaller transactions. Therefore transactions become cheaper.

Witness space has a 75% discount: 1 Byte in the Witness is counted as only 0.25 vBytes.
Therefore if there are many bytes that make use of this discount in a block, it bloats the block size. When a block is filled to the brim with witness data, it can go up to almost 4 MB.
With CISA, we would aggregate many signatures into one and therefore use less witness space.

It wouldn't stop data embedding, but at least actual monetary transactions would become more efficient and cheaper.

If we want to go even further and discourage data embedding, we could remove the witness discount. But that would probably be harder to get consensus on.

Before the witness discount, creating an output was cheaper than spending an input. The original purpose of the witness discount was to incentivize UTXO consolidation by making inputs cheaper than outputs. But with CISA, UTXO consolidation would naturally become cheaper by using less space. This might make the witness discount obsolete. But as I said, I expect some people to be opposed to removing the witness discount, even though I would prefer it.