I agree with your premise that many players would be against redshirting. However, Wisconsin routinely has redshirts for basketball - I know it's not the norm elsewhere, but it is there. The prime current example is Ethan Happ who redshirted in the 14-15 season when he would have been stuck behind Kaminsky, as well as Hayes and Dukan. It allowed him to practice against really good competition and put a year of work in the weight room. There have been many others in the past, going back to Brian Butch. Guys like Illikainen and Thomas are similar to Happ in that they're expected to be major contributors when it's "their turn", but there is a logjam of experienced players ahead of them and they have a long ways to go to be considered NBA-caliber. Only 60 guys get drafted each year - about a third are from overseas, and second rounders rarely pan out. The fringe 100-150 guys - which is who we're talking about here - aren't very likely to be leaving early. They have to develop. Whether a kid has the maturity to recognize that is a different question.
Some guys who see the writing on the wall in terms of low playing time choose to transfer, e.g., Riley Dearring and George Marshall (who did pretty well at So Dak St. getting them to the tourney). If Ilk and Thomas don't want to wait until it's their turn, they might transfer like Jarrod Uthoff did (who also redshirted at Wisconsin).