That is, in a 1080p v. 4K streaming contest, if you dedicate the same larger number of bits to the 1080p content as the 4K content, you'd get a better 1080p signal, too. With lossy compression, pixels aren't directly comparable, they have a quality, and low-quality 1080p pixels v. low-quality 4K pixels makes it hard to tell what differences are the format, and which are just the low quality in general.
(In other news, I consider the idea that streaming is obviously superior to disks to be a bit crazy. What disks have is higher quality pixels, and I expect that to continue to be true for a while. I've seen Bluray 1080p streams that are clearly superior to putatively 4K over-the-internet streams. And I've got DVDs that upscale to a higher quality than putatively 1080p streams of the same content.)
Far more important is the increased color gamut and HDR support, which does provide a noticeable increase in image quality. Even from those aforementioned dubious-quality streaming sources; the higher-gamut HDR images are a visible improvement over the NTSC-sunglasses we were all wearing without realizing it.