Having trouble intuitively understanding why complete circuits are necessary.

Trying to redistribute electric charge so it is not exactly balanced (equal density of positive and negative
charges everywhere), costs huge amounts of energy. Really massive amounts. Imbalances of
parts per billion generate ultra-high voltage fields (megavolts or so).

So to a good approximation charges cancel out everywhere. For a current to flow electrons in a wire have to
return to where they started, otherwise charge would accumulate at each end of the wire, taking
lots of energy and producing massive electric fields.

When you connect +ve of one battery to -ve of another there will be a very short burst of current
as the voltages equalize, but remember this is parts per trillion or smaller for fractions of a microsecond,
cancelling out whatever tiny imbalance their may have been.

When you connect +ve of a battery to its own -ve terminal the electrons keep flowing because of the work
done by the chemical reactions that sustains the voltage difference until all the chemicals are used up.

Consider the negative charge on all the conducting electrons in a gram of copper is about 10,000 coulombs,
balanced by the same amount of positive charge on the metal atoms. Then consider that a Van-def-Graff generator might struggle to get to 1 micro-coulomb of charge at 100's of kV... Unbalanced charges are
tiny tiny fractions of the balanced charge.

The electrons in the wire in low voltage circuits just shuffle around being replaced by the same amount of
charge - in other words current flows in a circuit (current electricity as opposed to static electricity).