I have an XP with 3 x 180w solar panels and 600 amp hours of battery life at 12v made up of 2x [2 x 300ah 6v].
We currently get way more solar than we need but when we were in a less sunny situation we used to get down to around 85% of our available power storage overnight, re-charging during the day but reducing an extra 5% each day we stayed in one place and were not receiving power from the truck s0, 85, 80, 75, 70% etc overnight.
We use a diesel cooktop – which still uses some electricity for the fan etc, and also diesel heating / hot water, which still uses electricity to move the air around. Both are Webasto.
We considered an induction cooktop but it would have been the only appliance that required more than a 1000w inverter, so we didn’t bother with the upgrade. The induction cooktops take a lot of juice but they do have the benefit of cooking extremely quickly, offsetting the power use. If you are a heat up and eat kind of cook then great. If you are a simmer kind of cook then not only does the induction use a chunk of power but it is also on or off; it pulses. So no simmer, just boil / off / boil / off .. repeat. Other XP owners have induction and like it though.
I think, in answer to your question, an all electric rig would be fine providing you had a decent battery pack / solar and had a decent bit of time on the road every other day to do the initial battery bulk charge, letting the solar top off the rest. Whether it would work would depend on drive time / solar ability in relation to your power useage.
On a side note, we plug in every month or so just to actually get the batteries to full charge. The charging cycle means that even driving daily and full sun solar, will not get you to a true full charge, which takes hours of continual small current.
2007 Dodge 3500
[5.9 Cummins, Stick Shift] + [XPCamper V1E]