This is not a specific problem with bluetooth, or wifi. This is a caching issue.
The Handy Wifi protocol loads most of the script to a toy, then just sends timing and playback updates to scrub to timing locations on the device. The handy bluetooth protocol sends commands one-by-one as they come in, which, with the inherent latency in Bluetooth LE, causes this lag.
If the handy cached the script to the device via bluetooth (which is doable), and could deal with the bit of timing jitter they’d get for playback updates in terms of bluetooth packet timing, this would not be a problem.