For an image processing program like the GIMP, the performance benefit could matter. I agree for an old word processor it would not. For an old spreadsheet program, again, you might want to run it as fast as possible.

I am thinking of the legacy systems you sometimes come across, where somebody set up a process in 1994 and it has hardly been touched since, but the volume of data it has to handle has grown a hundredfold.

You are saying to use the i386 architecture instead of x32, if you don't want to make the old code portable (or perhaps you don't even want to recompile it, having only an old executable). I agree that could be the most practical way forward.