I am going to give a very boring answer: It depends on the needs of your game.
tl;dr stuff to follow
More specifically–most IF games these days don’t have much in the way of timers. They may have atmospheric messages that happen every few turns or something, but mostly they’re on “Hollywood Time” as John calls it. For these games, there’s no reason not to have look and examine take a turn. There’s nothing particularly wrong with the atmospheric “You hear a crash of thunder!” message happening after the player has just examined something.
Some games have timed puzzles where you have to do something within a certain length of time. These games should… well, my opinion is that these games should not do that for the most part, but I’d also say that these games should probably not have “look” and “examine” take a turn. Often “look” and and “examine” are there to tell the player things they already know. It’s bad to have a situation where the player can lose because they type “look” to remind themselves of what’s in the room description, but they would’ve had enough time to complete the puzzle if they had just scrolled back and looked at the room description.
(Aside about what John said about examining–sometimes it definitely reveals something you can only see by looking closely, other times it’s just what you see by looking it, and it can even be something the PC knows very well but the player doesn’t. Consider this, from a famous My Apartment game:
This plant is your one claim to actual responsibility. The hyacinth sits by the window, soaking up sunlight (when it’s not night) and managing to thrive despite your lack of gardening skill. Although it looks a little parched at the moment.
Except for the very last sentence, that’s all stuff the PC doesn’t even need to look at the plant to realize!)
Then there are games where something is happening on a loop and the player needs to coordinate with the loop. This may be rare but I can think of at least one. In that case it’s probably important to have every command take a turn, so the player can get in synch with what’s happening. It’ll be easier to learn “This happens every four turns” than “This happens every four turns, not counting looking and examining.”
You can even have simulationist stuff that uses Variable Time Control to make different things take different amounts of time. This should be handled very carefully and should be clearly explained to the player if it’s going to make a big difference! The most important thing for all of these, I guess, is that if it makes a big difference it should be explained to the player or at least should be intuitive for them to figure out.
OK, though I said I kind of hate timed puzzles and I’ve barely written anything, I realize I’ve managed to do all four kinds of timer (or maybe this doesn’t match up?) My rationales:
Variable Time Control: A game about making tea and toast before someone wakes up, which I don’t think puts a lot of pressure on the players (because it’s not like you lose horribly if they wake up while the toast is still in the toaster). Having examining take less time than the actual tea-and-toast making steps was partly about moving things along when it was necessary. (“Tea and Toast”)
Look/inventory as a free action–there’s a game about rescuing a bunch of astronauts before the Mercury sun comes up on them. Timing was important here but look and inventory were strictly about reminding yourself of information that was already available to the player, so it didn’t seem right to have it take a turn. (I may have forgotten to tell the player that they were free actions.) (“Terminator”)
Everything takes a turn because of a loop–well, this game has a complicated time thing going on that would be spoily to explain here, but it would’ve been really confusing to the player if every action didn’t go into the normal time sequence, and if you got killed because you examined or looked at the wrong time, you could always undo. (“Faithful Companion”)
Everything takes a turn for other reasons: There’s a puzzle that kills you after a short countdown, and you have to find the right (and reasonably obvious) action to turn off the countdown, but everything else gets blocked while this is going on–so it didn’t seem reasonable to let the player just examine any old thing during the countdown, almost none of which would be relevant to turning the countdown off. (The cloak on the porch in Cragne Manor, which is totally optional anyway)