Every other team has already started searching
If the Bears were going to fire Eberflus, they should have already done it. With eight teams already looking for a new coach, the Bears would be behind the 8-ball if they decided to get started now. Teams are already scheduling interviews and the top candidates have multiple set up already.
The worst-case scenario would be firing Eberflus and then having to settle for a replacement. The allure of the Bears' job will always be a thing, but the team's top choice will likely be gone soon. Unless the front office has an under-the-radar target, the ship is close to sailing on landing the best of the best.