Photoshop LZW colors and sharpness

Sounds like you should be employing normal colour management workflows including calibrating your monitor, using appropriate profiles for your printer and so on.

Why doesn't compression without distorting any pixels and tones feel right to me?

What does it reduce without reducing the size of the image and colors?

By @Fetih

Perhaps it doesn't feel right to you because you don't understand lossless compression and perhaps only know of lossy compression such as JPEG.

There are different ways of encoding data, which may (or may not) make a file smaller in file size. Generally, the trade-off is in slower saving times than with uncompressed data.

Imagine the following fictitious example:

1, 2, 3, 4, 5, 6, 7, 8, 10, 15

vs

1-8, 10, 15

Nothing has been lost, both methods express the concept of the numbers 1 through to 8, however, the second is "more efficient" as it takes up less "space" than the other (but needs encoding and decoding to restore the missing range of digits from 2 to 7).

The easiest one to learn about is RLE:

https://en.wikipedia.org/wiki/Run-length_encoding

I'm not going to even try to explain lossless LZW or ZIP compression, you can read up on that yourself:

https://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch

https://www.techtarget.com/whatis/definition/LZW-compression