Warming up the PCB before desoldering may help. Best done with a regulated infrared preheating station, of course. If not available, using a good (regulated) heatgun may do the job as well. But it's important to be careful not to heat up the PCB too much. The temperature of the PCB has to remain below the temperature the solder is melting. I'd recommend approximately 150°C for SnPb40 solder (almost every arcade board of the 80s/90s). Prevent delaminating the PCB or stressing the components by overheating or boiling the PCB for a long period of time. As much as neccessary, as short as possible. The reason this helps is the soldering iron has to lift the temperature by e.g. 30° instead of 160° if not preheated, so much less power is required.
How good or bad desoldering works depends a lot on the PCB. Sometimes it's better to fill the holes again with new solder and remove it again at once afterwards instead of trying to get solder out of a hole where 3/4 of the solder has been removed already. Desolder wick also takes away a lot of heat, so a soldering station providing enough power is essential.
Despite working on PCBs for decades now, I still haven't found a perfect method that works all the time. Watch the PCB while doing and stop if there are beginning signs of delamination.