Or is there a technical issue than I'm overlooking? Strictly technical answer please. Thanks.
YES... It is a human interface challenge.
You can turn off the VHF or turn off the AIS and only use the single antenna with one unit at a time.
This is "technically" isolating the system input of the individual radios. This does not account for over-bleed or isolation filters of the individual radios. You may still find that the feedback in the shared antenna leads, damages one or both of the units. A detailed inspection of the unit wiring diagrams would be needed to provide a positive response.
Now to the real world. You are cruising along using the AIS on the antenna. Suddenly you have a heart emergency. Recognizing the danger your crew rushes to the radio to hail the Coast Guard. "MAY...." some one forgot to switch off the AIS before attempting to call out the Mayday... Now one or both of the systems are fried and you are in a world of hurt.
As a former radioman, use a powered splitter or use separate antennae.