Replacing the I-beam cursor system wide.

[. .]

Is it possible to replace the I-beam cursor system wide through X or 
Wayland (trying to think ahead here)?

In explanation, years ago I suggested, to deafening silence, that Open 
Office offer a block/blinking block or underscore/blinking underscore 
cursor.  However, I'd prefer no I-beam cursor in any application 
(browser, spreadsheet, email ... you name it).  If I understand 
correctly, X displays what the application directs.  Would it be 
possible to amend X to display a different cursor anytime it's directed 
by the application to display the I-beam?