LOG shouldn't be noisier, you're just seeing more of the noise in the shadows. After grading, all that should go back to normal.
Shooting LOG in low contrast situations where there's just a narrow band of luminosity in the scene - I'd agree with you there, but then you may still need to match colour to the daytime scenes with a specific LUT.
Sometimes you do need a wide dynamic range in low light at ISO 3200 as well, there might be a brightly lit interior in the shot or bright street lights.
Definitely ETTR in low light. Better to select a high ISO especially with a dual gain sensor, than to under expose at say, 400, and ramp up the shadow noise in post.