actually i think its the other way around - filters make it easier to get natural looking colours. with a filter, you are balancing the colours that are captured by the sensor. when shooting without a filter, the red channel has much lesser info compared to the blue and green channels.
in my experience, the best way is to shoot RAW files using a filter, then post process to get natural colours.
however, like you rightly pointed out, filters cut out light so you could lose at least 1/3 stop or more of light. and you will only be able to shoot ambient light, which means vis has to be good and keeping dives shallow. quite a lot of considerations when shooting with filters.
the cons of using a filter with a dslr set-up is that you can only rely on ambient light for the whole dive and cannot use strobes. otherwise the colours would come out looking really funky.