While working on my machine and rebuilding the flipper assemblies I have noticed that many of components wires are soldered to their connection points.

I suppose this is typical Pinball practice.

Why cant quick connectors be used?

For instance using quick connectors for the EOS switches, Lamp sockets and Solenoids?

Quick-connects add cost and another possible point of failure in a machine. I think costs were the key concern.

Quick Connectors aren't always as easy as they seem to be. Supposedly it'd be as simple as soldering the wire to one end of a connector, and then the connector should be as easy to work with as a phono plug for your stereo. In practice, the connectors are either way too tight (requiring a pair of pliers on each end to disconnect) or they are too loose, providing an extremely basic connection. When I first heard of them, I thought it'd be a good idea, but after buying 15 different matched pairs and types, I still haven't found any that actually did what they should for my purposes. Solder is simpler to work with for me, or perhaps I haven't found the right connector to use yet.