Speed chess (or blitz chess) has become popular in recent decades, but I think the standard tournament times are 2 to 2.5 hours, if I'm not mistaken. You might have gone to blitz tournaments, where yes, your inability to play quickly would have been a great handicap.
But blitz tournaments are not the only, or even the most popular type of tournament. When you see someone's chess rating (ie. 1700, 2000, etc), those are ratings at slow time controls. When someone is referred to as a "grandmaster", it refers to a title that is earned at slow time controls. The world chess championship is played at slow time controls. There are blitz tournaments, but they are not as popular. Blitz is very popular in clubs, though. You're right there.
My guess is that you couldn't leverage your superior slow chess skills to blitz because you just didn't practice much blitz (ie. short time controls or fast games) on your computer, or against human players. This is understandable, and is quite common. It takes some practice to get used to playing blitz. I'd bet you would have made a fine blitz player if you'd put in some time practicing it, and your slow chess skills would have helped you in blitz, as blitz and slow chess aren't different games, but blitz relies more on intuition as opposed to deep analysis. But both blitz and slow chess require good pattern recognition and memorization, so your aptitude in the slow chess would have helped you in blitz, once you got enough practice in playing more intuitively at faster speeds.
Finally, as far as chess computer these days go: just because the computer moves fast doesn't mean you have to move fast. You can set whatever time controls you want when you play against a computer -- hours, days, weeks, or even turn the clock off altogether. On the other hand, chess computers have gotten so good these days that unless you're a world class player, you're just not going to beat them at their highest difficulty settings, no matter how much time you have (unless you cheat). They're still good to practice with, and you can still play slow chess (even correspondence chess, where you mail or email moves to each other and take a long time to reply) against humans. I think if you look, you'll find plenty of slow chess fans around the world that you can play.
But blitz tournaments are not the only, or even the most popular type of tournament. When you see someone's chess rating (ie. 1700, 2000, etc), those are ratings at slow time controls. When someone is referred to as a "grandmaster", it refers to a title that is earned at slow time controls. The world chess championship is played at slow time controls. There are blitz tournaments, but they are not as popular. Blitz is very popular in clubs, though. You're right there.
My guess is that you couldn't leverage your superior slow chess skills to blitz because you just didn't practice much blitz (ie. short time controls or fast games) on your computer, or against human players. This is understandable, and is quite common. It takes some practice to get used to playing blitz. I'd bet you would have made a fine blitz player if you'd put in some time practicing it, and your slow chess skills would have helped you in blitz, as blitz and slow chess aren't different games, but blitz relies more on intuition as opposed to deep analysis. But both blitz and slow chess require good pattern recognition and memorization, so your aptitude in the slow chess would have helped you in blitz, once you got enough practice in playing more intuitively at faster speeds.
Finally, as far as chess computer these days go: just because the computer moves fast doesn't mean you have to move fast. You can set whatever time controls you want when you play against a computer -- hours, days, weeks, or even turn the clock off altogether. On the other hand, chess computers have gotten so good these days that unless you're a world class player, you're just not going to beat them at their highest difficulty settings, no matter how much time you have (unless you cheat). They're still good to practice with, and you can still play slow chess (even correspondence chess, where you mail or email moves to each other and take a long time to reply) against humans. I think if you look, you'll find plenty of slow chess fans around the world that you can play.