There's a downside to making the skewers too tight. It's bending the axle. This isn't a problem with wing nuts but is with quick release skewers. Therefore, one should make the skewers only as tight as necessary - to hold the wheel on the bike.

How much is necessary depends on the dropout type horizontal vs. vertical. Horizontal dropouts require the skewers to resist the twisting motion caused by the chain. Skewers designed from horizontal dropouts will usually be serated to resist the twisting.

Vertical dropouts don't require the skewer to be very tight. The rider's weight and the vertical dropout geometry alone will keep the wheel aligned in the frame.

You can ride without a skewer on a vertical dropout. I've done it twice. The first time was an oversight. I drove to a ride start and forgot to tighten the front wheel skewer, when I assembled my bike. I did not discover this until 35 miles into the ride. I came to a rest stop. I lifted the bike over a curb and the front wheel fell out. The second time was deliberate. My friend's rear skewer broke. His bike had horizontal dropouts. His bike could not be ridden. My bike had vertical dropouts. I gave him my skewer and rode without a rear skewer. No problems - although this time I was very careful to avoid any bumps in the road.