Your question may be simple but the solution is not. Although seeding all classes 1-32 may be a very slight improvement, it is easily the least important of the several flaws found in the current system. Similarly, simply putting the playoff separation of public schools and private schools to a vote would likely satisfy less than half of the individuals that have an opinion on this matter. It will not be accepted and people will not just move on.
A sophisticated solution is to meld the best of the competing alternatives into a single solution. Two such solutions have already been proposed on this message board. The first is titled "A Proposal for High School Football Playoffs" and can currently be found on page 2 of this message board. It is a comprehensive proposal addressing every issue in the current system that posters to this board have objected to. Perhaps its most important feature is an overhaul of the success factor, including the introduction of a success factor for public high schools. No proposal can hope to totally eliminate all complaints, but based on message board feedback the adoption of this proposal should greatly reduce the amount of dissatisfaction that is expressed towards the current system.
The second proposal is found in the thread titled "SF 10 Syc 0 F". That thread can currently be found on page 4 of this message board. The proposal is found on the first page of that thread and is dated November 16, 2024. The most important aspect of that proposal is that it would partially separate the CCL/ESCC from the playoffs. There are many details provided, but in a nutshell the CCL/ESCC would hold its own playoffs for the first three rounds with the winners then being introduced into the IHSA brackets at the semifinal round. Yes, it is innovative, and yes, it was not universally accepted by members of this board. However, it is a self-correcting plan that automatically adjusts to changing circumstances. It would likely be very well received by IHSA members.
Despite your modesty, you are well connected with a number of high school football coaches in the state of Illinois. If you were to submit either or both proposals to one or more coaches for their review and possible submission to the IHSA for a vote, some traction might finally be achieved on getting the system fixed. (I understand in most cases the coach will not have the final say for a particular school and will need to forward the proposal(s) to the athletic director and perhaps the principal.)
If one of the proposals is approved by the IHSA membership and some (perhaps many) private schools choose to leave the IHSA as a result, that would be their voluntary choice. That is a better course of action than the IHSA membership voting to expel private high schools from the IHSA.
The two proposals referred to in this message will provide a reasonable opportunity for general acceptance by IHSA members and the opportunity to move forward on a positive basis; not to mention producing a more competitive playoff experience.