No, but I don't think one can do it with IFR either? I was thinking of slot "windows" rather than specific times "to the minute".
The fact of the matter is that IFR flights
are regulated and VFR flights are not. There are no airspace-based slots for VFR flights, therefore a flightplan is not needed to secure one. While IFR FPLs for flights entirely outside controlled airspace are sent to CFMU anyway, it doesn't achieve anything from an ATFM point of view, and arguably complicates matters.
I don't deny this - but my understanding was that ATC is there to separate me from traffic which I cannot see. If you ask anyone who is interested in IMC flying - they would probably ask how ATC could help them. Maybe that's why some countries figured out there is indeed a safety advantage and therefore introduced Class-E.
Class E sounds like a "happy compromise" answer, but in fact the advantage is illusory. The idea of mandating an ATC service in IMC but not VMC sinks or swims on the efficacy of see-and-avoid in VMC. Even at GA speeds, see-and-avoid is effective in avoiding only a low proportion of potential collisions -- most are avoided simply by having low traffic density in the airspace and at the time in question. Thus when you follow through the logic, providing separation services between flights that elect to use them, regardless of weather conditions, is the best compromise.