So, flippers are more complicated than I thought; they have a microswitch and two coils in the solenoid for quick impulse response with low holding current. That's fascinating!
Also, flipper EOS switches are leaf switches, not microswitches.
Through the early 90s the flipper button switches were also leaf switches. In the early 90s some time after the introduction of the Fliptronics system by Williams/Bally, they switched to using a plastic opto-interrupter and U-shaped opto(s) rather than a leaf switch.
Games with upper flippers often used ganged leaf switches and later dual optos to allow independent "staged" control of lower and upper flippers on the same side of the machine. That allows you to press the flipper button in half way to engage only the lower flipper, and then all the way to also engage the upper flipper(s).
There are lots of good solenoid driver ICs around, but they're mostly sized for automotive applications. Pinball flippers typically need 5A at 50V, which is a lot to ask of an IC but no problem with an external power MOSFET. There are pinball boards for this. (http://www.allteksystems.com/products-mpu-replacements.html#...) No need to use electromechanical relays and put up with burned contacts any more.
(I'm interested in this problem because I restore old Teletype machines, which have similar electromagnet drive problems. The classical solutions are huge and inefficient by modern standards.)