Pump in a few hours of solar power and a late-day flight is likely to be bumpy. The other major advantage to an early start is that it provides more time to work out alternatives to get to the destination. Despite that excellent recommendation, several years ago business delayed my departure on a trip from St. Louis to Wichita until just after lunch. There was a strong cold front 100 miles west of Wichita but good VFR to the east. An isolated supercell lay across my route, but it was moving northeast along with the strong southwesterly flow aloft.
Thunderstorms generally move, develop, and dissipate.
Arrive too soon or too late and the arrival is likely to be uncomfortable, dangerous, or both. The briefer was emphatic about the potential for severe weather, but there were plenty of alternatives, so it seemed reasonable to start out. The first two-thirds of the IFR trip was in nearly clear skies with 30 miles' visibility. The big cell had moved north and was dissipating, but when I crossed the Kansas-Missouri border about 40 minutes away from Wichita, the sky became very energetic. Small cumulus were building rapidly into big ones.