I thought a big part of the reasoning for tilting trains (Talgo especially) was to enable increased speeds comfortably on unmodified tracks, is that an incorrect rationale?
Partially true.
The speed of a train in a curve is limited by four factors
1) passenger comfort, This can be alleviated by tilting
2) perpendicular track forces that can lead to increased wear on the rail, push the track out of alignment, or worse still, cause the wheel to climb the rail and derail. This can be alleviated by restricting the axle loading and seeking a low center of gravity. Tilting trains are generally lighter than regular trains. Talgo especially so
3) operational restrictions such as imposed by signalling distances, visibility, These need to be resolved by capital investments.
4) the track itself. If this is totally rickety, even the most hi-tech train in the world can't go much faster on it without endangering safety. Again, this needs capital investment
Many railroads have seen tilting trains as a quick fix and a low cost alternative to proper HSR, but by addressing some but not all of these points have failed to deliver the hoped for benefits, and thus end up with an expensive train running a schedule that a cheaper rnormal train could have done just as well.
This is not so much a problem in the US with its generous clearences but in Europe and especially the UK, tilting trains need to be narower than regular trains to allow space for the tilt and this leads to a compromised interior design with many users now viewing tilting trains as an inferior solution from the passenger perspective.
So in summary, if done properly, tilting trains can be a wonderful thing, but if not done properly they can be quite a botched job.
The initial inspiration behing the Talgo was by the way not about tilting. In fact the early generations of Talgo train did not tilt. It was originally about creating an ultra-lightweight train that could accelerate quickly with a low-powered locomotive.