When I learned about the concept of "just barely good enough" I was thrilled by it. Lots of people been using the expression "good enough" and to me it feels like a defeatist idea. "They did their best! It's good enough, isn't it?"
http://agilemodeling.com/essays/barelyGoodEnough.html
Given the constraints of the estimate we've made for a story that could really go much longer, except that we've only allocated two days... I think the problem you're hinting at is that different people have different ideas of what the Minimum Viable Product should look like.
Accordingly, on my team where we're all under-trained with respect to Project Management and mostly just making this shit up as we go along, we've identified several other points on the curve.
It's suggested that one should make some nominal efforts to identify, and stop for a sniff along the way to JBGE:
"that's definitely not good enough, try again"
"I'll know it when I see it, but I'm sure that isn't it"
"kinda-sorta good enough"
"that's nearly good enough, except for this one thing..."
Identifying some of these points along the way (and making sure you notice when you've arrived at them) in my opinion is a great way to help ensure you're not actually aiming for points somewhere deep on the wrong side of the curve.
The mediocre team also may have trouble getting to Just Barely Good Enough because of overshooting. But in my experience that's usually not the problem. Nobody is working far past JBGE into the wee hours of the "OMG this is too much, I love it but how long did it actually take?"
If anything, the feature has to be shelved or scrapped, or handed off to someone else, because it's taking too long due to an error in calculation of trajectory. Spending too much time on the wrong things. Incremental progress is the goal, and perfect is the mortal enemy of good.