Research is done by professors and students, not admins.
The overall average trend in the US is for administration costs to increase and instruction costs, relative to admin, to decrease [0]. Some universities will vary, but the trend is important to look at overall.
My point is that the article you linked to is not a data point supporting your assertion that tuition cost increases are caused by more admins.
A) Yale is a research-heavy university so the admin:student ratio shouldn't be expected to be constant. B) Yale's admin:faculty ratio decreased from 2003-2021, directly contradicting your claimed trend.
The overall average trend in the US is for administration costs to increase and instruction costs, relative to admin, to decrease [0]. Some universities will vary, but the trend is important to look at overall.