WWE.com has a video up revealing the only 8 Superstars to ever kick out of the Tombstone. To me, it was as interesting to look at WHEN the kickouts happened as it was to look at WHO kicked out. So the Undertaker debuted in late 1990. The first kickout was in 1998, by Kane. In between, he wrestled future HoFers like Hulk Hogan, Bret Hart, Kevin "Diesel" Nash, Mankind, "The Supreme Fighting Machine" Kama and Shawn Michaels. None of them kicked out of the Tombstone - though HBK would later.
So, up until 1998, the move was VERY protected. It was nearly a decade before the next Tombstone kickout: Batista at Survivor Series 2007 in a Hell in a Cell match. Still pretty darn protected. Before Batista, 'Taker wrestled guys like Austin, the Rock, Randy Orton, Kurt Angle...none of them kicking out of the finish. But after that, the next time was just months later at WrestleMania XXIV versus Edge. Then it was HBK the next year (and the year after that) at WrestleMania's XXV and XXVI. Then he wrestled Triple H two years in a row, and if you don't think Trips kicked out of the Tombstone at least a couple times, you haven't watched wrestling in the 2000s. The next year, Taker beat CM Punk, but not before Punk kicked out of a Tombstone. At WrestleMania XXX, Brock Lesnar put the 1 in 21-1 and started his own Streak of kicking out of a Tombstone in every match against the Undertaker.
Undertaker got back on track with a big pointless win over Bray Wyatt...who kicked out of a Tombstone. This year, thankfully, Shane-o-Mac did not do the same.
TL;DR: In the first 17 years of his WWF/WWE career, one man (Kane) kicked out of a Tombstone. Since then, 7 have (and 'Taker has worked a...let's call it "limited" schedule since then). I think that says a lot. Not even really about the Undertaker and the Tombstone. But just the HUGE difference in what a finishing move means now versus at other points during Taker's career. Now false finishes are a dime a dozen. Even Raw matches often see a finisher kickout. And at bigger "PPVs" you might need to hit your finish 2 or even 3 times to put away an opponent.
WayTL;DR: So what's the point of a finisher if hitting it doesn't finish the match?