Why is commercial, sliced, sandwich style bread so popular in the US and UK, as opposed to more traditional European loaves (like this Slovakian bread)?
I cannot speak to the historical trends in the UK, but in the US, the rise of commercial, sandwich style bread is part of a larger set of food trends that took place after World War II, into the 1950s.
Housewives were looking to reduce the amount of labor they spent in the kitchen, such as baking from scratch, while simultaneously there was a trend towards processed "scientific" products that were seen as pure and wholesome at the time. See this article from Smithsonian Magazine for more information.
I would argue that the modern is actually moving away to this with the "slow food" and "whole food" trend, and the rising availability of more traditional loaves in regular grocery stores, and increased awareness again of home baking. In fact, recently, whole wheat and whole grain bread has passed white bread in popularity according this article from the Chicago Tribune.
To put it bluntly, convenience, price and availability. While more artisan or rustic breads are available in supermarkets (where the vast majority of westerners shop, especially the US and UK), they are generally more expensive, a less convenient shape and size for sandwiches, and don't keep as well.
Having said that, in recent years in the countries mentioned, there has been an increasing interest in home baking of all kinds, including bread.
It's worth pointing out that some western countries like France and Italy still have a strong tradition of buying fresh bread daily.