In theory, yes, you would want just enough thermal paste to fill any gaps between the heatsink and die as the thermal conductivity of the heatsink (e.g. copper)

In theory, yes, you would want just enough thermal paste to fill any gaps between the heatsink and die as the thermal conductivity of the heatsink (e.g. copper) is much higher than that of the thermal paste. Unfortunately, I haven't been able to find much on the internet beyond forum posts and anecdotal evidence regarding the pump-out effect. It would be interesting to see a more scientific study of this.