Depends a lot on what you start with and on some of the other assumptions you make, but for seawater, the theoretical limit is probably ~3 kJ/kg, and the absolute state of the art full scale desalination is probably 11-14 kJ/kg
Given average water use per person in US is 310 liters/day (82 gallons) [1] and average electricity cost/kwh is $0.17 [2], and assuming 14 kJ/kg. 310 * (14 / 3600) * $0.17 = $0.20.
[1] https://www.epa.gov/watersense/statistics-and-facts
[2] https://www.bls.gov/regions/midwest/data/averageenergyprices...
This study found these uses for indoor residential use: 18 gpd toilet (~10 flushes), 15 gpd washer (~1 load every few days), 11 gpd shower (~5 minutes), 11 gpd from faucet (~5min of flow, this one surprises me), 9.5 gpd from leaks, 1 gpd dishwashing
that's 65gpd right there. A ten minute shower and slightly more frequent laundry would easily get you 82gpd on indoor use only, ignoring any irrigation / outdoor use.
Is that wild?
Perhaps in the sense of "on average, families have 1.6 children" (or whatever it is) — i.e, these are aggregate numbers, not to be taken as specific examples of actual households. Interpreting statistics can be tricky like that.
Also, to be fair, that study (I briefly looked) just lists toilet per-capita GPD in the quoted section ("Daily Per Capita Use"); it does not equate it to a number of flushes. They do have a whole section devoted to toilet flushes though — see "ULF Toilet Savings".