The main problem with upgrading the ground is that, even though it's obvious that the Kop is the most in need, we would realistically have to add the second tier to the South Stand first. That change could be done without closing the stand, whereas the Kop needs knocking down and completely re-doing, due to the poor (and cheap) foundation work done back in the 90s. That's at least one season, probably more, with almost 11k less capacity, which would mean a whole bunch of current season ticket holders not being able to go to home matches for a while. If we did the South Stand first, then we could probably cope with existing season ticket holders while the Kop is rebuilt. The only other option would be to ground share somewhere else for a year or more.
Indeed, it's more accurate to call Bramall Lane the site of the oldest professional football stadium in the world. The oldest stand is the Lane end (1966) but even that has had substantial work done to it since it opened, making the oldest complete stand the South Stand (1975.)
As a (probably unrealistic) hypothetical question, how would people feel if we built a brand new stadium that was still at Bramall Lane, like Spurs did with White Hart Lane, i.e. knock the whole lot down and replace it with something state of the art and with a big capacity?