Also note that the study you mentioned is comparing prices in 2018 with two recession recovery years (2011 and [edit: typo] 1988 - the year of the S&L crisis), which is an unfair comparison against 2018.
[0] - https://fred.stlouisfed.org/series/MEHOINUSWAA646N
[1] - https://www.huduser.gov/periodicals/ushmc/spring05/ushmc_05q...
If two partners are buying a house together (a fairly common occurrence) per capita ratios would treat both partners as an individual, but a household would help fix for that discrepancy.
Median household incomes take into account households of all sizes (1 person households to n-person households), and if you compare against median price, you can help reduce the risks of outliers tainting any comparison.