The wire process works fine, but the circuit board has to be designed differently for them.
Solder the through holes before the IC's and sockets are placed on the board.
Don't put through holes under surface mount IC's because the solder bump will hold the IC up in the air.
Don't use the pins of sockets as vias, as the top side of the pins under the socket can't be soldered.
Design the board with a separate through hole connected to the socket pin. It can be under the socket, if
it doesn't interfere with the body of the socket by holding it up in the air.
Use a tight fitting wire in the through hole so that it doesn't slip when the second side is soldered.
Attached is an image of an example pcb board designed with separate vias.
The vias are the pads marked with yellow circles.