Do flaps have a maximum speed limit but spoilers don't? Why?
Spoilers are used to shed energy when the aircraft is too fast or too high. That means they need to be used when the aircraft is flying fast and are designed accordingly.

On the other hand flaps are used to increase lift and when flying fast, there is plenty of lift, so there is no point in using flaps at high speed and therefore they are not designed for it.

Additionally flaps on large aircraft are more complicated mechanically. Spoilers only rotate around their forward edge, but flaps on large aircraft extend to the rear in addition to rotating downward.