...since the start of word processing, as it was the simpler option.

But see here:

"The suffixes -st (e.g. 21st), -nd or -d (e.g. 22nd or 22d), -rd or -d (e.g. 23rd or 23d), and -th (e.g. 24th) are used. Formerly, these indicators were superscripts (2nd, 34th) but by the late 20th century, formatting them on the line was favoured. The superscript style has, since the 1990s, been revived somewhat as some word processors format ordinal indicators as superscripts automatically." http://en.wikipedia.org/wiki/Masculine_ordinal

The above quotation is an example for why the "on the line" style is favoured. The original Wikipedia article uses the superscript here "were superscripts (2nd, 34th)", but when I copied the text and pasted it here, the superscript didn't appear.
But I'd say, if you can, go for the superscript.