Chess isn't popular because all major tournaments make it lack emotion. For some reason, all major tournaments are those of classic chess, that is, with high quality games that last 5 hours or more. The outcome of these high quality games at the highest play level is most typically a draw. This is totally broken and does not have a chance to make it to the mainstream public.
Now look at soccer, which has a bit of popularity in Europe and South America. At the higher level there are few goals scored but games are more often than not full of emotion. Just like chess, a small mistake (even a referee mistake) can determine the result of a game. Just like chess, it is a game of mistakes, but there is a major difference: things happen fast, sometimes faster than the eye can tell. The center back does not let the forward to think as much time as he wishes so that he can make the shoot of the century. Instead, he tackles him. The difference of level among a division and the division below is the time they have left to make a decision once they have the ball. The higher the division, the shorter the time to think.
To answer your question, FIDE does not try to make chess more popular because it is promoting the classic games, which are of no interest and of a lot less quality than two machines playing against each other with a regular computer. FIDE has been losing time trying to make chess an Olympic sport so that it can get funds by governments that are willing to increase their vanity each 4 years by getting Olympic medals.
If FIDE had any interest in making it more popular, the major tournaments where all money and fame are need to be of fast games, from 5 to 10 minutes by player, with lower quality but a lot more fun, and leave the perfect games for the machines.