The AD-E1 is nothing more than a gasket translation device. If your environment requires weather sealing, then the AD-E1 is required.
Correct up to this point.
If not, then you can just take the gasket off the offending unit and drive on. The 430EX III-RT is fully compatible precisely because it lacks the gasket. I own the R7 and atop it rests a ST-E3-RT -- sans gasket.
Not correct. There’s no need to remove the gasket. A weather-sealed flash is fully compatible with the new multifunction shoe, except (as you correctly state above) it won’t be weather-sealed unless the AD-E1 is used.
I routinely use my four 600EX-RT flashes (one mounted at a time, of course) with my R3. I have an AD-E1, but I haven’t needed it so far.
There was a lot of confusion over this initially, before the R3 was in anyone’s hands. If you removed the gasket from your ST-E3-RT, you probably won’t miss it but doing so wasn’t necessary.
Here is a 600EX mounted directly on the R3, you can see the flash’s gasket does not extend far enough forward to cover the front part of the hotshoe.
Here is the flash mounted with the AD-E1 in between, where everything is sealed.