Rather than 'too clever by half' formulas, why not support my request for a function that will divide a two-dimensional array into a collection of rows or of columns prior to any aggregation?

In this case

= MIN( BYROW( ArrayName ) )
would give a column array containing the minima.

That array could simply be embedded within the SUM to read

= SUM( MIN( BYROW( ArrayName ) ) )
This will get more important with dynamic arrays because the usual strategy of using relative references will need to accommodate dynamic spill regions.

In any case, it is not mathematically sound to request a summation over an array

A(I,J) without specifying which index to sum over. In my experience, the Excel assumption that you want both is the least useful.

https://excel.uservoice.com/forums/304921-excel-for-windows-desktop-application/suggestions/36151087-aggregate-2d-arrays-by-row-or-by-column-especiall
Other examples might include

= AND( BYROW( BooleanArray ) )
to test for a record that matches a set of criteria or

= SUM( BYCOLUMN( PeriodicData ) )
to sum financial data over a variable period.