I think whether this correction is done by the computer in the camera or in editing software the result is the same and you can dispense with the filter.
You are wrong, the results are very different. The sensors on these cameras often have up to a 16 bit color range that they can detect. But the file that it writes can only contain an 8 bit color range. The white balance setting, be it set manually, automatically, or automatically with a filter pushing it one way; centers the color range recorded to the file. So you have more of the colors you want in your recorded file, so you have less detail loss when you make your final adjustments.
Here is an example of the limited color range. The water was extremely green, and I wasn't expecting that so I didn't have the filter. I adjusted the colors as best as I could without losing too much quality, but you can see on the turtle's head where the colors are blown out because I ran color range to work with.
Now this isn't as big of a concern for still photographers, because raw shooting modes are common on photo cameras, in fact even the GoPro and some phones support a raw files. In fact it helps not just with color but exposure. I took some photos for my business and the woman was in more of a shadow than I wanted. I used a selection tool to pull her out into her own layer, and just made a small adjustment to brighten her up, and exported the file. When i was shooting JPG or slides I could never do that, I simply didn't have the available dynamic range.
But I highly doubt that we will ever see raw video on GoPro, the microsd cards simply don't have the write speeds. We might see HDR (10bit color) for 4K with the 11 or 12, but I don't know about anyone else, I would want to export HDR files too, so I am going to still have to worry about the recorded colors