Shouldn't this measure rest auto-adjust?

it sits, and IMHO rightfully, exactly where it starts in comparison with the measure above

There are no measure rests in the posted example - only half rests, and they are positioned correctly.

There are three similar looking types of rests in standard notation:

- half rest, aka minim rest - these sit above the line and always last exactly twice as long as a quarter / crotchet rest (two beats in n/4 time). These are aligned with other notes or rests that start on the same beat.

- whole rest, aka semi-breve rest - these sit above the line and last as long as four quarter / crothcet rests (four beats in n/4 time). These would normally be used as such only in measures that are not completely empty, and they too are aligned with other notes or rests that start on the same beat. Note because a whole rest in 4/4 time takes the entire measure, that means any measure in 4/4 time that contains a whole rest is completely empty, and thus shoudl not a whole rest. Instead, it should use the measure rest, described below.

- measure rest - looks exactly like a whole resT except that is centered in the measure. It indicates the measure is completely empty! Regardless of time signature. In 4/4 time, there really is no difference between a whole rest and a measure rest. But measure rests are always centered in the measure, whereas whole rests are aligned with the beat they start on (beat one). MuseScore will incorrectly create whole rests instead of measure rests when you copy and paste a passage that contains measure rests. I believe this has already been fixed for 2.0. Meanwhile, you can delete the incorrectly created whole rest, which will cause MuseScore to use the proper measure rest.