We have Paxton for door entry, one site has push to exit, other has swipe to exit with break glass override for emergencies.
We have Inventry for signing in with one reader in the entrance area.
When we had the systems installed I asked the same question but was told it it better to have 2 systems for a few reasons:
Staff will hold the door for each other, especially at busy times leading to them not clocking in or out being the main reason.
There is also an area for parents in reception, any staff want to speak to them would be clocked out.