Old standard is not the limitation of modern good performing equipment. If you want the best performance you have you pair it with suitable front end. In this case, 1kohm isn't really asking too much. Sure I get it, versatility is something to care about. But in some cases, majority of modern/or very new dacs are very capable of doing 2v to 1kohm.You can gain up to10dB of s/n, depending on the input opamp (FET vs. bipolar) by going to a lower value pot for the volume control (10k to 1k in this case). However, as has been stated, 1k ohm is generally considered too low by the industry as a whole for an input impedance. If you use a buffer with high input impedance to drive the 1k pot, then it works great. So, no, I don't think it's a good idea to just swap the pot for a much lower value. Some kind of low noise, low distortion buffer has to be added to drive the low Z pot. Now the issue becomes one of designing an awesome buffer that can handle the full output from a DAC or CD player, which is another story.
On the input buffer, not necessarily the best idea because interference can definitely go in and then be buffered, 50hz main hum being pucked up by cable is definitely a thing. So imo it's still better to have low input impedance. Maybe not 1kohm, 2kohm is good choice too, if input buffer is used/ or often time combined with gain stage.
It's somewhat a trade off but not necessarily. Because most mid tier dacs only has -110db something thd+n. The top tier ones have -125db. So relatively speaking the output buffer still produce lower distortion than whole system.
Also I guess that's not the main problem with 1k pot. Many dac has 100ohm output impedance meaning we lose 1/10 of the signal level. I don't know why they have it. But to me that's the only thing I consider whether to use 1k pot or not.
In the end, from my measurements and testing, 1kohm is an acceptable option. For most 10k is fine too. But 50k or 100k? Not acceptable in my book.