I will acknowledge some pros of the straight up "skill check" approach:
You think the DM should be a neutral arbiter of the game. Skill checks create an illusion that the DM is just implementing the rules, and not making judgment calls. (To make this real and not an illusion, there would also need to be an agreed upon deterministic method for determining DCs.)
You believe that you should always have a 1/20 chance of accomplishing anything.
Some people have expressed that finding creative/novel ways of overcoming challenges feels like "player skill" instead of "character skill". I disagree, but if you're in that camp then giving a fixed DC no matter how the challenge is handled would make sense.
You just don't trust your DM to be a good arbiter, and/or you don't trust your players to not harass the DM until they get their way.
EDIT: Oh, and one more: if you're simply used to playing this way, it's something new you don't have to learn. I guess that's only a pro if you don't want to have to learn new things, though.