When creating a new matrix, it would be faster, and more natural to type ctrl+m 2,3
rather than use both row and column fields

For me personally, the default for columns would best be 1, that is what I use more often than anything else.

I also find filling matrices slow and difficult. It would be much easier to comma delimit data in columns, and semi-colon delimit rows. This would make it easy to fill either across or down. When reaching the end of a row/column, it would wrap to the next (regardless of "," or ";" )

The problem with tab is that it is with keys 1,2,3 + tab is it's a left hand cack handed stretch to the tab key that gets capslock every time, for me. - so I have to do it slowly.

Using comma is left-right-left-right and flows smoothly. (This is the same reason that // is my favourite comment character regardless of language - it flows whereas eg. shift+# never does)

Currently empty matrix creation is CTRL+M #rows TAB #columns RETURN (6 keystokes like in your suggestion) - BTW ^ is already assigned to the exponentiation operator

Wrote

For me personally, the default for columns would best be 1, that is what I use more often than anything else.

... at will, wherever ... ONE keystroke.
Fill manually or address.