Why can't current go through two voltage source junction?
Your intuition is correct, but explaining why clearly might be trickier.

Current only flows in a loop. There is no loop that includes your crossed out path.

If you wanted to consider that your crossed out path was in fact two conductors, and current flowed out and back along the same wire, then conservation of charge for each of the left hand and right hand bunch of nodes nodes means that the leftwards and rightwards current through that path are equal, and therefore cancel out to zero.

Or more simply, conservation of charge on each bunch of nodes means that no current flows between them.