It's not really a fallacy. However most people think playing == improving. This is not the case.

The best players I know, and the fastest improving players I know, all review their gameplay and take notes on the mistakes they made. They watch other high skill / pro players and take notes on what they do. They practice PERFECTLY, over and over and over (i.e. executing a combo flawlessly 20 times in a row, if you make a mistake, start over. Now do something else for an hour, then flawlessly do the combo 20 times in a row again). They find good players to play with in high stakes situations, such as tournaments or money matches.

Most people don't improve very much because they aren't actively trying to improve. I know many people who are at roughly where they were a year ago, or just marginally higher.

Almost nobody does what you suggest and even doing this does not guarantee you will consistently improve. You don't know what you don't know, and masters are often not vocal about intricacies of their strategy. Many of them are geniuses, particularly in strategy type games, and as such people with much lower G factor probably have a slim chance of ever reaching that level. I know several of them myself. Gave them visual IQ tests like ravens progressive matrices. I know the validity is not very high but of the 6 people diamond 1 or higher in League of Legends I gave the test to, not a single one scored below 135.