If the text can be 'sharp' when you are in the footer why can't it remain so when you are working on the main page?
I'm willing to bet that if MS development was to reply to this question they would call the issue you identified, "clear text in footer", as a "defect" or BUG. If Word was working as they planned it to, EVERYTHING would be blurry! Apparently, for some
reason the footer is not using the "right" / new graphic display system.
Now that you have identified the "problem", it is probably on their "to-do" list to "fix" (what the rest of the world would call BREAK) it. Just be glad that it is likely a very low priority, does not affect many people.
Sacha's fix is the best. UPGRADE back to 2010 or earlier and
DEMAND a
**$$$**REFUND $$$
for the defective product, Office 2013!