Well they don't, at least not in our view!
Ever since I started in the inventory business, now on the way to 15 years ago, letting agents have generally charged the landlord for the inventory and charged the tenant for the check-out.
This would have made sense pre-TDS, but since April 2007 I've argued that it should be the tenant paying for this due to the tenant's deposit being protected against the inventory.
It has been when communicating with agents that I get a mixed bag of responses with some confused as to why. However when I say that by charging the other way around they may have a competitive edge on their rivals, they see why.
Of the agents I deal with, most have taken this method on-board and agree this is a much better way of working. It certainly means that when competing with agents with lower fees they can slice off some of the original charge from the up-front amount paid.
Either way it seems sensible to us that a tenant should pay for the inventory and where required the check-in, and the agent pays for the mid-term and the landlord for the check-out.