I'm with Foxhole on this one. Closed riser stairs form, in essence, a sort of crooked I-beam girder in which all the elements interconnect and are glued and nailed/screwed together. Remove the risers (and their associated wedges) and the staircase will become substantially less stiff and much, much weaker. The risers and treads are grooved into the stringers and in addition the risers are grooved into the undersides of the treads, just beneath the nosing) and may or may not be grooved into the tops of the treads as well. If you remove the risers you will need to infill these grooves as they will be rather unsightly. This picture of a pair of routed stringers illustrates the extent of the grooving (and even before routers or stair making machines the same general pattern was made by the joiner, by hand, using a selection of saws and chisels):
In order to hold the wedges which are used to assemble the stairs, those grooves on the stringer are actually cut with a dovetail cutter (as can be discerned on the above photo). The completed underside of a tread should look something like this (Although with a few less gaps!):
In point of fact modern open riser staircases still feature narrow riser elements beneath the fronts of the treads - this is to stiffen the treads as well as to reduce the opening beneath each tread to less than 100mm (it is a statutory requirement for gaps between treads or between spindles to be less than 100mm in order to prevent children having accidents by slipping through)
TBH if you want open risers on a straight flight it is safer and arguably less work to rip out the old stairs and simply replace them (at least from a chippie's perspective)
