It puts the DM in a more difficult position for a lot of kinds of checks. If you don't call for a roll when a player wants to check something, you're communicating it's either so simple or so complicated they cannot succeed or fail, or you're communicating to your players the question isn't important. IE there is no trap, or something useful connected to identifying something, etc..
So if a player says they check a chest for traps, and you don't call for a roll, then you're communicating there is no trap on that chest. You're communicating something you don't necessarily want the players to know by responding with no check. So you're more inclined to allow a check each time, so that when it does matter your players have an opportunity to detect it.
So yes of course it's the DMs call, but that doesn't really address the issue. It just highlights which person has to deal with the issue.