100 steppers. Seriously.
At least one pulse pin and one direction pin (if using 4-wire steppers and a board like the A4988) makes for 200 output pins, of which 100 need careful timing to produce the pulses for the correct movement. Way too much for a single board.
That's a lot of work to wire up. Power wires to the controller boards, wires from boards to steppers, etc. Lots of wiring.
You can do maybe 10 steppers per Arduino, one master to send high-level commands to the individual Arduinos.
That's a lot of current - steppers take 1-2A each, so that's 100-200A.
That's a lot of interference - the current control by the stepper drivers mostly.
Servos sound like a very good alternative indeed - a few turns left and right implies you're moving things by a little bit, and that's exactly what a servo can do very well. Not sure if you can nicely control that many from a single Arduino (you probably want to control the movement carefully) but it sounds quite feasible. You still have to deal with the current and interference of course.