This is quite common in Blighty; there is no need for another ticket (outside some time restricted fares where the ability to stop is limited). Indeed, it can be nice hopping off at a new city for a mooch around if you have time to do so.

(Only slightly off-topic; We have the phenomenon of 'split tickets', where it can be cheaper to buy two tickets from A --> B --> C rather than one ticket from A --> C even when the train stops at B anyway! You don't even need to get out of the train at B if you don't wish to do so. Our ticketing system is a mess.)

All saver tickets in German (which is what most people use), and most TGV tickets (even non saver) are bound to specific trains at specific times.

https://www.bahn.de/faq/was-bedeutet-zugbindung

The UK is the odd exception here.

Flexible tickets are becoming unaffordable for certain journeys such as those on the ECML with LNER (aka The Government)