I'd accept survey data (blind taste tests) but real science would be better. If coffee tastes better when served in heated cups, why? Is it chemistry? Or is this all opinion based on nothing?
I doubt that heating the cup influences the the actual flavor of the coffee from a chemistry perspective, however, it turns out that there is a specific preferred temperature range in which consumers prefer their coffee. The warm cup probably helps ensure one is getting their coffee in that window for a longer period of time, thus it is perceived as tasting better.
I would say it is mostly about maintaining an optimal serving temperature for as long as possible. If you asked a number of people, most would probably agree that cold coffee doesn’t ”taste” good. While chemically there is hardly a difference, perception of flavor depends on temperature. (Which is why white wine is served chilled while red wine is served at room temperature.) So you want to make sure it stays close to brewing temperature. That is particularly challenging when you have some 50 ml of espresso in a tiny cup – heat is lost not only to the cup, but also to the environment due to the small volume.
Cranking up the brewing temperature to compensate for loss of temperature comes with other side effects, as this will alter the chemical composition of the coffee – you get aromatics which would not get extracted at all (or to a much lesser amount) at optimal brewing temperature, whereas others may evaporate more quickly at higher temperatures, all of which have an impact on flavor.
So the solution is to get the cup close to the optimal brewing/serving temperature so as little heat as possible is lost to the cup. Also, traditional espresso cups have fairly thick walls in order to increase their thermal capacity. That helps the cup, and the coffee inside it, stay warm for longer.
I expect this is a simple case of using "taste" when meaning "flavour", that is, not just taste but the whole experience of ingesting something. I expect most people would agree that ~50°C milk/vodka/tea/coffee/orange juice has a very different flavour than ~20°C or ~5°C, even though the chemicals are the same.
Tongues sense chemicals differently depending on the temperature (a quick search finds Link Between Taste And Temperature Focus Of "Thermal Taste," A New Discovery By Yale Scientists, Heat as a Factor in the Perception of Taste, Smell, and Oral Sensation, Temperature Affects Human Sweet Taste via At Least Two Mechanisms, Stimulus-Dependent Effects of Temperature on Bitter Taste in Humans). Notice for example how lukewarm water seems to enhance any impurities, while really cold water seems to taste basically nothing.
(A successful barista should probably optimise for flavour rather than just taste.)