This is not really correct as a blanket statement. As it pertains to the LiPo batteries we use predominately in RC, I will mostly agree with your statement however as I would never use anything but a dedicated charger with algorithms designed specifically for charging lithium cells.
I have used a Rivergate 30-amp power supply, a competition electronics 24-amp power supply and a Muchmore Powermaster to charge 12-volt car batteries throughout the years. A charger is basically a power supply with more sophisticated circuitry. If you have a power supply with both variable voltage and current, you can easily charge a wide range of batteries. Here is a how-to:
http://www.learningaboutelectronics....C-power-supply

As others have stated, the primary reason these days for a separate DC power supply is to have more power on tap. Chargers with AC input (AKA built-in power supply) are usually relegated to charging at relatively low power compared to their DC counterparts. The largest I recall seeing is the single output Turnigy Rekator 20-amp/300 watt. While this is quite powerful for an AC charger, it is small compared to something like an iCharger 406DUO, which has dual outputs with up to 40 amps (1,000 watts) of charging power each.
We would probably need to look back to the roots of RC to see why most stuff runs on DC power. Back in the day our tracks were temporary setups in parking lots and the like. The only power available was the battery under the hood of your real car, so necessarily everything ran off 12 volt DC power. As we evolved and started building permanent outdoor and even indoor tracks AC power was more accessible, but we already had all of these 12-volt DC devices, so the obvious answer was the 12-volt power supply adopted to our hobby.
To this day, I'm guessing there are still quite a few facilities where people are bringing generators or large deep cycle batteries to power their DC chargers, tire truers, pit lights etc because AC power is not easily accessible. Perhaps they race at a different indoor facility in the winter where AC power is readily available. You wouldn't want to buy all the same gear twice - one set for outdoor use on DC power and one set for indoor use on AC power, so the power supply makes perfect sense. It's a lot smaller and lighter than lugging a deep cycle 12-volt battery into the pit area.
In my personal pit area, my power supply typically runs my charger, pit light and tire truer. Back in the day of NiCd and NiMh batteries and brushed motors you could find a few more items running off power supplies like comm lathes and discharging/balancing trays. If each of these devices needed their own built-in supply they would physically all be much larger.