Why is there so much "pulling" involved in English driving?

There seems to a variety of terminology around the verb "to pull" in English driving, which always puzzles me. Here are some examples:

• to pull out of/into something: to drive out of/into
• to pull over: (transitive: to stop; especially police, right?)
• to pull in (intransitive: to arrive at a destination or come to a stop)
• to pull away: e.g., maneuver the vehicle out of its parking spot and resume driving

Do these phrases have some (common) historical origin (such as, being pulled by a horse before cars were motorized), or did I miss some very general meaning of "to pull" when learning English?

Solution 1:

I suspect this is a hang-over from animal-drawn conveyances. The wagon would be pulled in to the side of the road in order to stop within causing obstruction.

Solution 2:

Merriam-Webster Unabridged, in its Synonym Discussion for the verb form of pull, notes:

draw, drag, haul, hale, tug, tow: pull is a general term meaning to move in the direction of the person or thing exerting force

It's interesting to note that, seen in this light, the direction you're trying to go is what's exerting the force on your vehicle (e.g. when you're pulling into traffic, the traffic is what is supplying the pull; your vehicle has simply latched onto it, metaphorically speaking).