This is also how the original Doom's networking worked[0], and still used to implement RTS networking[1] where the number of entities to be synchronized is very large compared to the amount of input.

0. http://fabiensanglard.net/doom3_documentation/The-DOOM-III-N...

1. http://www.gamasutra.com/view/feature/131503/1500_archers_on... 1500 archers is the classic treatment but also see dissenting opinion here: https://medium.com/@treeform/dont-use-lockstep-in-rts-games-...