Perhaps, but it has nowhere near the history and prominence of Kentucky basketball. Besides, can anyone here besides Suns name players on the UK football team?? I can name some on the basketball team but I couldn't name a single player on the Kentucky football team. Plus I didn't know/care about any of the items that you listed above.
There are football schools and there are basketball schools. Very few, if any, are perpetually good at both. Kentucky is clearly a basketball school. (And a damn fine one at that)