Okay, so let me preface this by saying that I'm not necessarily arguing but just doing the math for my own country just because it's fun. It's also not super precise.

If you drive a lot, you'd be buying diesel not petrol. Usually. But that's just me nitpicking, I assume you mean ICEs in general.

It depends on your region too. In some, EVs are so much cheaper to run it's not funny, in some they're comparable.

In my country, if you choose the correct power company for home electricity, a public charger during daytime is 0.333€/kWh. If you use a cheaper power company at home, you pay 0.37€/kWh at the biggest chain of public chargers. This of course assumes you use the cheaper, <=100 kW chargers. Faster ones are more expensive so we'll just pretend they don't exist. Charging at home varies from 0.05 to 5€/kWh if you have a variable rate package or if you lock yourself in to a price it's probably around 0.15 if you locked in a few years ago for a long period, or 0.2 if you lock in now. This is including the transmission fees and everything.

So let's say bare minimum 0.15 unless you want to time it by hour, and maximum 0.33 because most people aren't stupid and unplug their shit when the prices skyrocket for an hour or 2, so realistically home charging SHOULD always be cheaper than public charging.

An MB EQE sedan will do roughly 20 kWh/100km driving on a highway at 120km/h with AC and stuff on - normal driving, not super eco, but also not very wasteful. That can be anywhere between 3 euros per 100 km (VERY cheap compared to ICE) and 6.6 EUR per 100 km. Comparable E-Class diesel sedan or wagon will do 4.5-5 l/100km these days at same speeds, so 6€ per 100 km at the fuel price I got last time, 4€ at the best price I can get, or 7 for the worst prices seen this year.

Let's assume you have a great electricity price locked in and you only ever charge at home, and that fuel prices go back up and stay there. This is a 4€ difference in the price for 100 km, in the EV's favor. A huge difference tbh. But the price difference for cheapest EQE and cheapest diesel E-Class is 10k in favor of the diesel. At this price difference, it takes 250k km for the power savings to pay off. A lot of these cars get sold off before the first owner even reaches that mileage.

This math changes significantly with used cars, though. Cheapest BMW i4 I could find is 43k for a 2023. Cheapest diesel 4 series is 40k (and has more kilometers actually). At 3k price difference it takes only 75k km to pay off the difference assuming similar efficiency ratings for both, I cba to look it up. I wanted to do i5 and 5 series, but the i5s are so new they haven't really depreciated yet.

And if you use public chargers exclusively, well, it'll essentially never pay off at current prices. But that could change in the future.

Another thing to consider, though, is that here you're not really getting a "driver's car" with the ICE. Diesels are work horses and inline 4s particularly aren't anything special. The EVs, both the Mercedes and BMW, have significantly more power. You kinda get more for your money there, I was just doing a purely financial comparison, while keeping to German cars because that's pretty much all I drive usually (may be changing this though, I'm eyeing a hybrid Lexus as my stepping stone car between my diesel A6 and whatever EV I'll buy when my finances have recovered from a shitty marriage)