Postprocessing and filtering do not do the same things. For relatively minor adjustments, either can be used with comparable results as you have shown. Filtering works by selectively removing light so if a filter is working the way you want then it is removing light that you don't want. That is a positive thing, not a negative one as you have asserted.
In an ideal world, digital cameras would have infinite dynamic range, infinite resolution, true color representation and no quantization loss. In that naive but common view of how digital works, postprocessing can do everything that filtering can without penalty. In that sense you are correct but that is not what we have.
What really happens in a digital camera is that the image is quantized in intensity and color as well as in two dimensions. Cameras are of limited dynamic range and have a remarkably limited color system modelled after the deficiencies of our eyesight. A huge amount of information is irrecoverably lost in the digital conversion of the image. When the plan is to do large color corrections in post, as you are suggesting, rather than optically using filters, what you are doing is further discarding what data is left. For minor adjustments that isn't a problem but for major ones it is.
Looking at this another way, lets say we are shooting an ambient light shot at moderate depths without filters. In this arbitrary, hypothetical case, we may have red light 6 stops surpressed from the surface, yellows 3 stops surpressed, greens at full brightness and blues 1 stop down. What the photographic result is depends on the subject matter, but its easy to see that the red channel in our sensor may well be 4 stops underexposed, the blue channel one stop underexposed, and the green channel properly exposed assuming we nailed our exposure. Of course, we may well be tempted to underexpose the water and make matters even worse. If this sounds farfetched, I assure you it is not. Light conditions at 60'/20m are worse than this!
Hopefully you can see by this example that what you are doing without filters is severely underexposing reds in order not to blow out greens, then cranking up reds in post in a desperate attempt to color balance after the fact. You should know that underexposing 4 or 6 or 8 stops results in a totally unusable image yet this is EXACTLY what you are doing when shooting unfiltered ambient except in the shallowest water. The result will be heavy chroma noise and banding/tonality problems. You will also get unreliable color due to metamers.
Instead, ideally you want to expose reds, blues, and greens as fully as you can by surpressing the overabundant green (and, to a lesser extent, blues, cyans, oranges, yellows) so that all sensors "fill up" regardless of color. You do this by using the proper filters. With a good filter matched to the type of water, time of day, and depth of shooting, you can achieve surprisingly great color, although you may need high ISO to achieve it. Video shooters with the right gear can get great color in excess of 100 feet because those cameras have remarkably powerful white balance systems. Post processing cannot do that because it is working with the data that's left, not all the data that there was.
As I said before, filters also provide creative options in mixed light shooting not easily achieved in post processing. Some people, myself included, prefer blue water and strongly desire to surpress greens in the background. Others may choose to surpress background color, enhance background color, or perhaps even enhance the green water in unique locations. All this is possible with complimentary filtering. It is essentially impossible with postprocessing. These techniques do not require matching filters to conditions but they do require matching filters on lens and strobe. Not all strobes, or lenses, take filters well.
Hopefully, you see that I didn't miss your point. Filters ARE "necessarily better" than post but they are not desirable or appropriate for all conditions. It is hard to justify the use of filters for macro, for low light black and white imaging, for shallow water, or for wide angle where the color the photographer gets without filters is simply what he wants. Filters are a useful tool to have in the toolbox, not always interesting to photographers, but for which there isn't a substitute. No videographer would do without them.
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