Typical Sci-Fi wormholes have that problem, but there are nevertheless valid GR solutions that look a heckuvalot like wormholes. And they do obey all those cons

Typical Sci-Fi wormholes have that problem, but there are nevertheless valid GR solutions that look a heckuvalot like wormholes. And they do obey all those conservation laws. One can think of it as the wormhole mouths being objects (made out of space rather than matter) that accumulate and lose conserved quantities like mass and momentum and charge as objects enter or leave them, or you can think of it as lines of force getting stretched out to pass through the wormhole mouths whenever an object moves through them, since the fields can't just shear off. Incidentally, this generally means that you have to be careful about balancing the mass flow in each direction through your wormhole, lest one mouth develop negative mass (and presumably antigravity) from too much stuff leaving it and the other mouth end up shrouded in a black hole.