You're assuming that the ice and gravel etc. is stationary with respect to the Sun. Why would that be? Also, what's doing the "picking up", in this example?
assuming that particles are at random motions, ( they have a bias in the solar system of course) zero velocity difference would be the mean. Pickup, and holding on is by gravity, a lot easier if the object to be pulled in matches (on average) the speed of the matter around it. Think of a meteoroid that comes straight down matching the earth orbital and rotational speed.
Because of the interplay of orbit and spin velocities there are from zero to 2Vo areas exposed on Saturn, Jupiter to the environment at all times. begging for an easy entry.
Stretching effects? What are you talking about?
The tidal effect that stretches the earth, water air surface too. It gets less the further you are from the sun. but
during rotation, matter near Saturn's equator, while maintaining constant rotational speed and distance, constant gravity effect to Saturn's center, ~lose all orbital speed with respect to the Sun. That means a stretch toward the sun, through the unopposed pull of gravity from the Sun. A lifting like our high tides, but with a different cause, a temporary
loss of orbital velocity. On the night side, the spin speed is added to the orbital velocity at the equator, again causing a stretching because of the temporarily gained
higher orbital velocity there. (two high tides circling the earth too) .
Dynamic tides on Saturn, "distance difference" tides on earth.
Eastward launches are easier from the equator because the ground speed at the equator can be used to provide some of the velocity needed to attain orbit or to escape the planet's gravity. This effect doesn't vary whether the launch is carried out at night or during the day.
Perhaps that is true with aimed-for earth orbit satellites, but when leaving earth orbit for the outer solar system and beyond, why would you forego that 30 km/sec +500 m/sec speed you already have naturally? as a matter of fact, if you launched at 30 km/second eastward in the daytime, you would be at
standstill with the solar field, heading straight up in a radius to the sun like the particles of Saturn at noon at the equator.
Shedding of mud etc. from a tyre is no more efficient at the top of the wheel than at the bottom. Relative to the centre of the wheel, the mud is travelling at the same speed at all points on the outside of the tyre. If it has to overcome the "stickiness" between the mud and the tyre by using the "centrifugal" force, then it does so in the same way at any point on the tyre. The speed relative to the road is irrelevant to this.
Let us consider it to be relevant. After the zero contact speed of tire/ road lodging, what comes into play is the acceleration/ inertia of the ice and gravel during holding and possible shedding. The material pressed into the groove at standstill is accelerated to twice the speed of the vehicle inside the fender. That pick up was only possible because of the matching velocities on the road. Of course, you are right, once in rotation it could be shed anywhere.
except on a planet, which, like in a rollercoaster
outside loop, highest point is at the convex side of an orbit, where the centrifugal forces of both rotation and revolution
add up on the outside, subtract on the inside (the road). so, it is not a stretch to say, top shedding is favoured.
Better minds had fun like this about bigger issues in Copenhagen.