+1 for at least an option.
Not knowing the DC also helps weak-willed people such as myself to not save-scum checks. If you know you failed the DC by just 1 then you (I) might be very very tempted to reload, especially if the character has a super-high bonus (5e's bounded accuracy+d20 system = incredibly variable results). But if you don't know the actual DC, for all you know reloading to succeed would take a lot of effort or be impossible, so you'll (I'll) be happier to just go with the flow.
And yes, blablablah "you can just not savescum" blahblah.
Agree. Save scumming is an "option", but should never be required to get critical checks in a game. If you don't know what the DC is, then you MIGHT save scum once, but then if you fail again, well, maybe there's a story reason for it.