It's fine if they really block the door, or make it clear why you can't enter. Making a wall, painting a door texture on it is anything but creative and reasonable. Adding a huge lock, chains, or a few boards is all it needs
Another cliché is what was present since Wolfenstein 3-D: The player begins the world/empire-saving quest only with the absolute minimal supplies! A sidearm & knife, no additional supplies, no medikits, no nothing. Yes, I know, in these cases, the hero always starts as a prisoner or a last survivor of a team, and this is necessary to retain the game's progressivity, but this is still a highly popularized phenomenon in FPS games.
Timed levels are fine, if the countdown actually has some purpose. Like...a nuclear reactor is melting down (sounds fitting in such topic), a friend of yours will be executed, the enemy wants to blow up a bridge, or something like that. If the time limit is there just to make you move faster, it is actually contra-productive - the player wants to hurry, he skips important supplies, has no time to find secret areas with important powerups, and messes up jumps, or gets killed by enemies as fighting them would slow him down. I was never really fond of time-runners, I don't know, I like to do perfect runs on a level (100% kill, 100% items, 100% secret), but there are of course the speedrunners, who has no problems with rushing to the exit dead on time
I guess it is a matter of taste.
Continues and lives serve no purpose if there is a save system. It's a small leftover from the arcade-era, where the game's purpose was to swallow more and more quarters from you, as you pointed out. Unfortunately, there are still some games, which don't let you save the game, and uses checkpoints instead (yes, FPS games too), so it's not really a fashion-fad.