> Tilt trains exist to allow higher speed service on older lines where tipping would be a safety problem.
That isn’t true. No train network is going to allow train to operate at speed, if the safety of those trains depends on non-failure of a complex tilting mechanism. Having a tilting mechanism fail or jam before a corner (which has happened) can not result in a high speed derailment. That risk is simply unacceptable on modern railway.
Tilting trains make it possible to run at higher speeds on older lines by allowing older lines to have the camber on corners increased to accommodate the higher speeds. But the camber can’t increased enough to hit optimal amount of camber without make the rail unusable to older trains.
Tilting trains provide a useful compromise. Increase the camber enough for stability (but not comfort), while keeping the camber acceptable for older trains, then make up the rest of the tilt with carriage tilting mechanism. The total amount of tilt is then comfortable for passengers. There is a minor safety element provided by tilting trains, in that lateral forces in cornering are lower, thus passengers are less likely to fall, and items won’t come of tables. But the tilting mechanism certainly is a safety critical element to running faster on old lines.
It’s also worth mentioning that carriages on passenger trains have a pretty low center of gravity, as all the heavy equipment (motors, bogies, breaks, suspension) sits below the passenger compartment. As a result tilting a passenger train won’t significantly move its center of gravity, so impact on total train stability is going to pretty minor.