That (electronic) analog computers have integrators is, as I have read, the whole reason analog computers existed—stuck around. Integration is ideal for simulating forces like gravity, etc. over time.

Early experimental X-planes (like the X-15, for example) had flight simulators that were completely analog—modeling the forces of lift, etc. (In the 1970's, there was even a commercial analog flight simulator sold [1].)

[1] https://inspire.eaa.org/2022/02/16/eaas-attic-atc-510-person...