It isn't just multiple layers, but also multiple fields within a layer. You could pull out some of the def's from
Field Statistics and repurpose them should you want to automate beyond what you could do with the summary statistics tools. It really depends on whether you just need the basic statistical parameters or you wish to get frequency distributions and other measures like skewness and kurtosis for the data. The shell functions are there, should you be adept at coding them within a layer list or for multiple layers for a particular field.
I did something like that before.
I had 4 table and I wanted to do summarize for all tables in one table
and I did like the below picture , I made summarize for each table then I did final summarize for merged table.
but all table had same fields that I used in summarize. This is important