It's not as simple as just replacing "your" copper line. You have to take into account that a typical cable (called a multi-core copper cable) actually carries many individual pairs. So it's not a matter of just replacing one. Perhaps you might get lucky in the future if a fault is found and they have to replace it as no spare pairs available - though they will probably replace it with the standard gauge.
Replacing D-side (from the distribution point) would be much more possible since, in most circumstances, it only has two pairs (and most premises are actually only using one pair). Though the typical distance which it has to cover would not have much scope for benefit unless it was actually faulty. Besides, I don't think Openreach will want to touch it unless there is a fault.
If there was a service for replacing cabling, it would be expensive - people with FTTPoD availability would probably just get better value by going through with a group project with their neighbours and utilise government subsidies for discounts. Though if you could somehow pay for a thicker gauge it would benefit places which have aluminium in the network more than those who have standard-gauge copper.
I have a somewhat good connection so perhaps I do not qualify to speak on behalf of those who are receiving a mere few hundred kilobits. But if I went back to ADSLx, I wouldn't opt for it since I know I would have to reach into my pocket for thousands of pounds. Also, we should be looking towards full fibre and not holding on to xDSL technologies - though maintaining existing infrastructure is fine as long as it is necessity.
Edit: Added missing word (oops!)