This does work on local networks, and it also allows a work around for remote (VPN) connections, which screen sharing doesn't work for. I screen shared with another local computer, not running 10.12.4, and opened Remote desktop on it. Established a VPN connection on that computer, and I can now use Remote Desktop truly remotely, which is how I use it 99% of the time, until Apple fixes this bug.
BTW, I also called support to report this, and since it was a beta version, they wanted nothing to do with it, and suggested reverting to 10.12.3 via a time capsule back, which is not an option considering the volume of work that would have to be re-done since the update. I guess the only thing to do is cobb along until it is fixed, hopefully soon.