As someone who make be suffering due to this issue, here is what I think.
If it is a line fault then it clearly at BT issue. The practical problem is that this has to accessed through the ISP interface, which can be highly tedious.
If the issue if it is DSL/Chipset code is tougher. In an ideal world your line characteristics would be measured, e.g for noise margin variations throughout the day, attenuation etc. Dependent on the characteristics measured then either the ISP or BT should recommend a selection of compatible modems or routers, plus a realistic assessment of what speed a customer can expect. This assumes that the ISP/BT knows how different routers behave with different line characteristics. I would guess that many ISP's do not have this information, or possibly the equipment or desire to acquire it. BT must have the equipment and technical expertise to do this, but they seem reluctant to publish any in-house testing. So, if the customer has a less than perfect line which many clearly do particularly in more rural areas, he may welll find himself in position of having to buy or borrow several routers to see if he can find one that works. This process is likely to result in complaints to ISP's plus BT engineer call outs, to say nothing of acute frustration for the customer, who is likely to end up feeling that he is stuck between a rock and a hard place (ISP & BT), and that neither of them give a F***. For my money BT is the obvious choice for providing this information. They maybe reluctant on confidentiality grounds, but if they could classify the line on some scale or other and then recommend a selection of routers for a particular class of line, then I feel that confidentiality becomes less of a problem. Yes I know it's more work for them, but they'll save on call outs. Just needs a bit of recording kit you plug in to your line for a week before you go onto broadband.