Just spotted the second tab that allows me to buy more doors and reduce the cooldown time. Maybe that tab should be the first one the player gets to see? Otherwise they'd just be waiting to buy their first worker instead. Or maybe highlight any tabs where you can already buy something.
The feeling of slowness seems to stem (atleast I personally found so) from the workers having this odd cooldown between opening doors. IMHO they should just dash from door to door whenever one is available instead of standing around for several seconds in between. Otherwise the speed upgrade just kinda feels like "meh".
Otherwise I like the concept of an incremental game about doors! Very interesting.