We had bi-mode trains for many generations. it was called "changing locomotives".
There used to be a whole range of through services which ran on both electric and diesel tracks, which have now been lost. A typical example was the Scotland to Birmingham services, which used to change to diesel at New Street and continue to the South-West. All now lost, the service from Scotland to Birmingham now continues to ... Euston, just duplicating the main WCML service. In fact, it seems to be used to sell through Advance tickets from London to Scotland on, enabling the direct service to be reduced.
The other alternative that developed was to run diesels for hundreds of miles under the wires, just to get on to the final destination. Hence HSTs running through from Kings Cross to Edinburgh. This also has been used to minimise the number of electric units built. The whole of the ECML wiring from Peterborough to Edinburgh, about 300 miles, has been used for the last 25 years by, as I understand it, no more than 29 Class 91 units, and the bulk of services throughout that section are diesel.