Back when such rumors initially began circulating, it was believed that the driving force behind Apple's desire to cut Intel out of the equation was simply that they were looking to increase their profits. Under the conditions of the current arrangement, Apple pays 5 percent of its profits to Intel in exchange for use of that company's chips. That, combined with the fact that using Intel chips makes it relatively easier for competitors to copy Apple's innovations combines to create a compelling reason.
Nothing has come of those rumors for more than a decade, but the most recent iteration of the rumor may have some teeth to it. This is considering Intel's ongoing troubles with the Spectre and Meltdown vulnerabilities that impact all Intel chips made during the last decade. Put that together with the above, and suddenly it seems like Apple has a lot of incentive to want to make a change.
The company's stock took a hit on the heels of the rumor, but most in the Apple community feel it would be a net benefit to the company. Not only would it give their products a competitive edge, but it would also allow Apple more control over their product development roadmap and ecosystem.
A recent Bloomberg report notes that Mac Pro laptops are slated to begin shipping with an Apple proprietary chip in the place of Intel's hardware beginning next year. In addition, according to the latest buzz, Apple plans to complete the transition across their entire product line by the year 2020.
More information on this topic as it becomes available.