I have already been playing with this as a manufacturer of BLE power switches.
It does allow for cross-platform BLE access leveraging JavaScript in the browser. The experience of someone gives permanent access is similar to running an app on a phone.
This means you can do a scan request from the browser and all BLE devices respond. Or you can silently listen to advertisements. I don't think you can only give access to particular devices and for example hide the fact that you have a Fitbit or Apple watch.
For smart home applications it is cool for configuration but not for daily use. You don't want anything rely on the user opening up a browser. Apps much more naturally run in the background so the downtime of the browser is a serious hurdle.
Every day I'm shocked by new BLE devices coming in that leak information or are improperly protected. I would only give permissions to sites that you would definitely trust with this.
Something that can come out of this is better attention to multi-device access to BLE devices. Keys that are set up for bonding can not be shared easily with other users. Apple brings its usual Apple-only solution in the form of Homekit, but it would be better to have keys that can be shared across platforms. If the browser becomes also a player this is gonna be important.