You might think an agreement to waive the fees up front will make the bids come in lower. Don't count on it. The fees are usually included in the contractors' and subcontractors' budgets when they bid on a job. If the fees are waived, they'll just make more profit. Inspectors may let things slide because they figure it's just another public project and without fees it doesn't make any difference.
Fees serve as a record of what's done and the costs that are incurred.
Contractors can fudge on reporting all the details of the work to inspectors so they can save fees and pocket the difference. The schools should be eager to guard against that possibility. These are school buildings, built to serve the children of Avon Lake. The work in building them should be thoroughly and properly inspected. You get what you pay for.