There are many possibilities as to why old recordings can sound bright.
If they are really old, like transcription discs or 78's, it is probably due to bad mastering choices made by the sound restoration engineer and mastering engineer. It has become a bad habit to no-noise the hell out of such recordings instead of judiciously choosing the playback equipment and playback curves and settings. Bad choices and the use of noise reduction results in a pinched or thin sound. It has been my experience that a well transferred 78 or transcription disc can sound really, really good - nothing at all like the stuff most people think when they hear 78RPM.
If they are more modern - anything from the tape era - it can be due to playback machines, pre-amps, bad mastering, etc. There are many reasons why a recording can sound bright. The primary blame should go to the mastering engineer as the mastering engineer has the final call on the sound quality. Patsy Cline & Linda Thompson should sound warm and life-like - not bright at all. Based on the artists you posted, I'm inclined to think that it is due to bad mastering choices by the mastering engineer.
A good example of the mastering engineer's influence are the RVG remasters. Some of those titles have 4 different masterings or more. Check out the RVG of Blue Train. Compare the RVG Blue Train to Ron McMaster's mastering of Blue Train. Then compare both of those to the XRCD mastering. Then compare those to the recent Analogue Production release as mastered by Steve Hoffman. They all came from the exact same tape and yet they all sound radically different. Why? Different mastering engineers! Same thing with "Cool Struttin'" by Sonny Clark.
The most modern recordings, digital recordings, sound analytical and are usually missing a bit of warmth straight from the source. However, they should not sound bright either.
In short - whether it's an old transcription disc or a modern digital recording - the result of what we hear is directly influenced by the mastering engineer. It's all in the mastering. The biggest influence on what you hear isn't really your system...it's the mastering.