Persian blinds: why the headrail is open at the top
The upper rail of the blinds is made as an open topped assembly because the inside operational parts of the unit can be easily snapped into place when the blinds are manufactured. Since almost all blinds of this type are custom ordered to width they are manufactured from very long raw material pieces that are cut size when the order is being fulfilled. 

Another aspect is that when the width of the blinds exceeds a certain amount there are center brackets that have to be able to clip into the upper side of the rail from the back so that the center brackets can remain hidden. (At least this is the case with some better looking styles....the center support showing from your exploded parts list picture leaves a somewhat ugly bottom flange of the bracket showing when the blinds have been installed). 

When the blinds have been installed up against the top of the window frame there is not too much chance for dust to accumulate inside the upper rail. I've replaced old blinds in my house that were in place for decades and had little or no dust in the upper channel. If the blind unit is one that uses a valence piece across the front to hide the rail that acts as an air flow baffle to keep dust as well. 

If you live in an area where dust is an extreme problem I am pretty sure that you will have many more short term problems with dust accumulation than inside the rail. If you must take some action to prevent any dust accumulation inside the rail you could choose to apply a narrow strip of self adhesive foam stripping to the two top edges of the rail before sliding it into place at installation. Such stripping would need to be cut away in the areas where the holding brackets are located. You would also want to have such installation use a valence piece in front so that the foam stripping does not stick out like a sore thumb.