Why the absence of Soviet battleships ended the type

Did battleships leave service when they did because the Soviet Union never commissioned its own?

Probably: once the Soviet battleship threat failed to appear, other navies had no peer capital ship against which new battleships were worth building.

The answer treats the type's end as a reciprocal procurement decision. A navy maintains an expensive capital ship partly to defeat the enemy equivalent; when the Soviet Union did not field that equivalent, the reason for Western counterbuilding weakened sharply. Technology mattered, but the missing opponent helped close the procurement loop.