It can improve the anonymity by a great deal. I also don't know how much will the exchanges and financial regulators (dis)like this (isn't Monero out of the major exchanges in Japan?).
I also don't know much about the other benefits, it can help the multisig, but I don't know how much and some simple explanation for start could help.
I'll also add a link I've found, but didn't read it all yet, since it contains too many references to things I don't know yet https://medium.com/digitalassetresearch/schnorr-signatures-the-inevitability-of-privacy-in-bitcoin-b2f45a1f7287
This fork won't be enough to really push BTC to the levels of XMR and Dash, but it's a pretty good leap in the privacy section, and I learn't a lot from this.
Nice post.