Not as many as you think, a water heater only has 3 times the electrical capacity of a standard wall outlet. So probably less than 6-10 Keurigs, but you'd need them on 4-5 (or more) separate circuits otherwise you'd blow the breakers.

If your average house only has one person showering at a time an 18 kW 3.51 GPM Tankless Electric Water Heater would work. It would cost about $500.

To replace that with Keurigs would take some work. They draw 900 to 1500 watts depending on model. So it would take between 20 and 12 Keurigs to match the power draw. I'm not sure what the inlet/outlet tubing diameters are but it seems some replacement parts labeled 1/4" so that's half a gallon per minute max. You'd need 7 or 8 running in parallel to move enough water. Probably 21 900 watt Keurigs running in groups of 3 would come closest.

I estimate about $2000 in Keurigs plus another few hundred dollars in fittings and a lot of time to reproduce a purpose built $500 water heater.

And of course Keurigs break frequently and you'd definitely void any warranty.

Good luck!

Oddly specific question

12 ounces in a Keurig.

5120 ounces in a 40 gallon hot water heater.

Around 427.

Okay SO, this depends on if you can refill them with your water line continually or not. I’m assuming yes as otherwise someone’s answered a swap from a 40 gallon heater.

They do about 12oz in a minute from a quick Google.

Normal tankless water heater is about 3gal/minute. Which is about 400oz.

So, 400/12 gives is 33.33, so since we probably want to make sure we hit at least that, I’d round up to 34. Would need a LOT more electricity for that, as noted by another poster below. Probably more than is actually run to most houses.

Note: unsure how it’ll run without coffee in it, the flow is likely improved and thus you could possibly cut it down by quite a lot, especially with some modification to allow it to flow directly from the heating source in the keurigs you could definitely cut it down.

Like heating your kitchen by opening your fridge door. If it isn't enough, add fridges!

You should factor in battery backups for each coffee maker.