Many people use other projections all the time, particularly people in such fields as general and human geography. In those fields the Mercator projection is just one of many projections.

Ultimately speaking, no projection will accurately represent what the Earth's landmasses really look like. This is because the Earth is a 3d object. A globe will always be the best way to accurately represent our planet. Or a virtual globe - computer software can render a lot of issues relating to projections rather obsolete.

Nonetheless the Mercator projection is definitely very popular. It isn't without purpose - the projection accurately reflects the sea distance between landmasses (unlike other projections) bearings, which made it very useful for sailors. Considering that world maps were refined during the age of exploration thanks to the exploits of people who mainly got around places via sailing, it makes sense that the projection became common. And honestly, the projection isn't that bad for its time. Things to the far north and far south are comically distorted, but otherwise it isn't too terrible. Of course, most people today aren't the navigators on ships, so I do think that historical inertia, or quite simply popularity, has a lot to do with the prevalence of the Mercator projection. If you see maps using the Mercator projection whilst growing up then it will sort of ingrain itself in your mind as the true map of the Earth. I've never really been able to get used to the Gall-Peters Projection just because it sort of instinctively looks wrong to me (well, that and the fact that most people who have argued for it do so for reasons beyond that of geography). History textbooks have started to use other projections, or a combination of different projections, though, which certainly helps.