If you've already copied all your CDs to hard drive I'd say stick with it, there's no intrinsic reason why a CD player would offer better quality (although depending on the CD player it might sound a bit different in presentation).

If local streaming really did offer an intrinsic SQ advantage I'd possibly go with it, but there's no reason why it should.

My reasons for sticking with playing physical CDs instead of coping them onto a hard drive have nothing to do with better sound quality.

Probably should point out that copying a CD onto a hard drive or to any other format is illegal in the UK. Although that's not why I don't do it.