Can galvanic isolation be performed at the user interface (UI)?
Some devices can be made that way. However little things like the keyboard or an LED or a crack in the display exposing conductors could kill the user if they are not insulated to a high standard, so it is difficult to make a device of much complexity that meets modern safety standards. 

Also the low supply current can be a major issue. For that reason, even devices that have no UI at all (eg. Wemo WiFi controlled outlet) will still use an off-line switching power supply. 

For something like a stove, a relatively expensive appliance, I would wager that the control circuitry would almost certainly be galvanically isolated (but check before assuming that, of course, if it could cause danger).