Why don't they reuse old lift shafts to improve accessibility. Quite a few stations had lifts that were converted to escalators. I was standing on the Piccadilly line platform at South Kensington as you an actually see where there lift shaft was. I would have though it would be cheaper to reuse the old one than build from new ?
In many cases the lift shafts have been utilised for other purposes- either for ventilation or equipment rooms. A good example of this is Holborn - one contains a fan shaft, the other a traction substation. These sorts of things are not-at-all cheap to move elsewhere, although it’s perfectly feasible if the budget is there.
Likewise some lift shafts have been breached for features like escalator shafts - Stockwell I think is an example of this, where the 1920s escalator shaft cuts right through the 1890 lift shaft. In this case re-use of the lift shaft would be virtually impossible.
Then there’s another issue that in many cases the old lift shafts don’t align to the location of the current surface building - Chancery Lane and St Paul’s are two examples of this. The former comes up in the old surface building, the latter in the middle of a road junction.
Finally it’s also the case that many lift shafts didn’t come down all the way to the platforms, so without further work this doesn’t provide a step-free solution in itself.
Doubtless there are a few where it could be done reasonably practically - however in many cases I suspect it’s not quite that simple. And bear in mind TFL is financially broke at present thanks to the Mayor of London, Sadiq Khan, and some other factors.