I'll add this: There's most likely a better coach out there right now that would've helped more that would taken the job. However (like you partially said), the pool is extremely limited by lateness of the available position, unwillingness of many to accept a lame duck position, and of course quality of job UIUC can offer.
I think the reason Lovie mentioned they want to take their time next offseason to conduct a true search is because of those points. If they were to do a real search right now (which is what would've been needed to find a better candidate (I know other's might disagree but these kind of positions are not highly, visibly desirable)) it would cost many man hours. Man hours that could be spent bettering the team immediately. Instead of what probably would've amounted to 2 man weeks worth of search, discovery, interview, and hire of someone (keep in mind they might still end at the same conclusion they came to), where as by promoting Miles, took probably about a days worth of work. You get a guy who knows the system and it's not like this kind of move is some sort of major talent dropoff.
Yes, he promoted Miles partially because he was his son, and you'd probably be right to speculate that if an identical candidate was not his son, there were others better suited already in the GA pool, but again, Miles isn't some guy off the street, and the talent difference in GA's is minimal.