iserith
Magic Wordsmith
Typically I see a bit of both. Players straight up claiming stuff and waiting for the DM to stop them or Players claiming outlandish things and rolling automatically since they doubt the DM will just let them. However at my table, we tend to "time out" and plan who rolls, who helps, and who acts as auxiliary.
Cleric: The murder dropped this religious pendant in the struggle, you say? As a cleric, I probably know with deity it relates to and that will tell us where to look. So which deity?
DM: Roll Intelligence for it.
Cleric: Time out. I'm rolling as I have the highest mod for religion.
Rogue: I'll help you.
Paladin: I'll roll too in case you roll double 3s again.
Cleric: Shut up.
Wizard: What did the pendant look like again?
DM: It's a dagger with a jagged edge on a bronze plated disc. There is a faint imprinting of a hand on it.
Wizard: I'm going to roll History to recall any history of that image and narrow down the guessing. 16.
DM: Ummm... You recall the Jagged Edge Alliance of the Age of Conquest.
Cleric: Age of Conquest, eh? Then all modern religious imagery wouldn't apply. That would make it easier... right?
DM: Somewhat. You know its not a newer symbol. (I'll drop the DC)
Cleric: 10 and 18
Paladin: 11
DM: The cleric notices that the old symbol is of Vultura, the goddess of scavengers, peddlers, and street folk from back when the empire was strongest.
Paladin: Guess we're going to that part of town.
In my games, getting the benefits of the Help action would require the player of the character who is helping to be specific about how he or she is actually helping. Based on the stated goal and approach, it may help, may not help, or I might ask for an ability check (though this last bit tends to be fairly rare in practice).
So Rogue and Paladin are going to have to tell me what they're specifically doing to help Cleric or else they contribute nothing. Wizard is clearly helping in this example in my view and would impart advantage to Cleric's roll. I would, however, ask the player to refrain from asking to make ability checks because (1) that's my job and (2) why would you ask the DM for a chance to fail?
Doing this a couple times is generally enough to stop players from asking for checks and to be explicit about the things they are doing so I can adjudicate their actions more easily. It also adds more context to the scene which makes for more interesting storytelling in my view.