It would be possible and very flexible, and certainly more powerful than the current system. But we would loose the convenience of having one date, which we need for query answering (or we could default to the lower or upper bound, or the middle, but all of these are a bit arbitrary).
I believe it would be more profitable to build a query system which always queries for the range. This would work for interval-only values (see my comment on the wiki page) as well as for value with interval.
I don't see this as a big overhead. It is more a problem for ordering, but internally, wikidata could store a "midpoint" value for intervals where no explicit central value is given, and use these for ordering purposes.
I think it would be great if the system is consistent for quantities, dates, geographical longitude/latitude, etc.
Gregor