How do thermal tapes transfer heat despite their low thermal conductivity?
Heat sinking compounds/tapes are less conductive than metals but are orders of magnitude better than air. The main goal of these interfaces is to fill in the gaps between the solid interface between your heat source and sink. Without such compounds air pockets would form and the thermal interface would be poor. See the image below (source). The compound takes up any space between rough interfaces. Compare thermal interface options using the table at end of description and you will see that the compounds make sense.



A single solid piece of copper or aluminum mountain directly to the chip die would certainly heat sink better but the issue is it would short out all the circuitry, thus epoxy encapsulation must be used for an isolating interface and as a result then some compound to interface to a metal heat sink.

When cost is a non-issue even more novel thermal interfaces can be developed. I have head of Chemical Vapor Deposition diamond used in certain packages as the diamond is superior to an epoxy interface but still has insulating properties. Example source, tho I have never personally used such devices. 

Thermal Conductivity Table: 

Air Thermal Conductivity: ~26mW/mK

EMC Packacging Compound: ~ 2-4W/mK

Thermal Compound Thermal Conductivity High Grade: 8.5 W/mK 

Aluminum: 205 W/mK

Copper: 385 W/mK

Diamond: 2200 W/mK