One critique of your preference would be that if a player wanted to stealthily pick a lock, find the map in the house and get out without being seen that could easily be 4+ skill checks. An initial stealth check on entering. A lockpick check. An investigation check. A stealth check on the exit. I know from a probabilistic perspective that you've just plummeted the characters chances for full success. I'm also sure we could think of other checks to throw in there. I doubt you keep adding checks in actual play because of the probability for failure issue. Which means that you simply choose to elide certain checks, meaning anything you elided is no longer a possible failure state in the fiction. In some sense, picking cost after a single failed check is more fair and leaves more of the possibilities on the time from how you operate in practice vs conceptually.
Depends on how they approach the obstacles, but aren't most adventure scenarios a series of obstacles?
No single failure should mean complete failure, but if you fail often enough then yes the characters may not achieve their goal. It's why I don't make world-ending scenarios or have one linear path the characters must follow. Sometimes the best laid plans of mice and men go awry.