For those that are genuinely interested in how it works, have a peruse of these pages from a system that actually uses distance based pricing. The most relevant bit is the 'regular ticket' tab.
Of note is that longer distance fares are cheaper per km than short journeys, also that special offers and advance ticketing are all available as well as extensive rover tickets, railcards for heavy users, excellent family leisure tickets etc.
If anybody is in any doubt regarding the complexity of the Czech rail network, I have attached a link to their system map for reference.
When tickets are sold, the general route is clearly printed on them. If an excess is needed, it's quickly worked out by the computerised ticket machines carried by the conductors. The system does have some complications, but they aren't in my opinion even close to the level of oddness that we have. I doubt there are 'Fares Workshops' in the Czech Republic (Czechia?)

.
Of course, as Yorkie has rightly stated, applying such a system to the UK will not happen because the administration involved in making such a huge change would be unjustifiable in time and expense!
Anyway, here are the links
https://www.cd.cz/en/typy-jizdenek/vnitrostatni-jizdenky/default.htm
Fare chart-
https://www.cd.cz/assets/info/cim-se-ridime/tr-10-zmena-18_priloha-1_cenik-1_cb.pdf
Network map-
https://www.cd.cz/jizdni-rad/tratove-jizdni-rady/files/cz-mapacr-171210-01.pdf
No NFM, no routing guide, no arguments! No penalties for leaving the train early, no inconsistent time restrictions, no positive or negative easements to catch public and staff out, if you want to use a longer route you simply pay the difference. Common sense is applied in regard to slight route km variations (eg in a Rotherham Central or Masborough situation). Sadly there are no nice dirt cheap obscure 'permitted routes' for us enthusiasts to enjoy, but the rover and ranger selection more than makes up for that!
I do understand that our railways are often at and over capacity, but I think that stemming demand by raising prices can be applied to any system of fares, also I'm not suggesting that we use these EXACT fares in the UK- our levels of subsidy, wages and expenses would require a rather different £/km figure- don't ask me what that would be because I'm not and never will be party to necessary data to work that one out!
Posted only for interest, any arguments please don't yell at me, email the Czech government and tell them they've got it all wrong lol!
PS the km distances are all listed in the freely available line timetables
https://www.cd.cz/jizdni-rad/tratove-jizdni-rady/