I thought from the opposite point of view. When the noise exceeds and overlays the original signal, there is no more data to be recovered from these low levels. But I'm not a noise specialist. It probably depends on the type of noise. These are interesting things.
I prefer 16bit due to capacity and easier handling of files. Even for 16bit, the quantization noise is several times smaller than the noise of an old cassette. Probably more important is to set the right recording levels as Gutbucket explained. But I agree with you, If I had a very rare recording, then I would transfer it to 24bit.