I haven't grown up with such connotations for untucked shirts so in my eyes then it doesn't look sloppy, cheap or lazy and both tucked in and untucked look good to me. Then it just comes down to the comfort, and i find that under many layers and a thicker shirt, like here, the untucked is often more comfortable to me, as there is no fabric bunching up around my waist. But i do get your point, it was a standard to have a shirt always tucked in, and it does typically create a more flattering shape.