Grip between tires and track pavement provided entirely by suspension and tires. Mechanical grip is very important on slow speed track like Monaco and Hungary, in slow corners where a speed is lover then 130-150 Km/h and during start phase of the race. Also, during jumping over curve skirts, if your car doesn't have enough mechanical grip, you can loose precious time fighting oversteer or understeer.
Aerodynamical grip and mechanical grip are very important, and good F1 car should have as much as possible amount of both. If you miss mechanical grip you are slow and car is undrivable in slow corners and tracks like Monaco or Hungaroring.
If you miss aerodynamically grip, your car will be unstable and undrivable on fast parts of the track.