There's a lot of legitimate criticism of Groce as an X's and O's coach, and people are suggesting bringing in someone who has very little track record on X's and O's?
Depends on what you think the biggest problem with this program and Groce has been. If you believe that his biggest problem is X's and O's, and we have no major recruiting gaps at key positions, for a long time nevertheless, then fine.
But there is probably another group that thinks that Groce's biggest problem has been his inability to recruit quality B1G level talent at PG and C/post (in addition to injuries). For 4 years now, although his overall recruiting at other positions has been fine, although not great. That does not mean that his X's and O's have been stellar either.
Recruiting is a necessary, but not sufficient condition. Especially at Illinois. Unless you can recruit, and recruit with the best, you will fail. You can even look at the history, Illinois' best teams (e.g., 89, 05, 01) included talent, independent of just rankings. Actually better talent that Groce has been able to get at other positions.
Experience as a HC is definitely a plus, but does not guarantee or negate X's and O's ability. Neither does it guarantee recruiting. But you have to hire someone who at least has a reputation as a recruiter and has charisma to attract recruits.
Now, you can say I want the sure thing, a very experienced coach who has a great track record as an X's and O's coach, has charisma, and is also known as a great recruiter. But those will be the top "hot names" in the recruiting profession and history shows we have not been able to attract those (e.g., Smart, Stevens). So unless you can close the deal with those, you will take some risk, one way or another.