In a medieval or modern-day setting this seems - to say the very least - unrealistic.
Does your modern-day setting have a mechanic to track credit ratings? Vaccinations? Familiarity with a wide range of cuisines (whether as consumer or as cook)?
Does your fantasy setting have a mechanic to track holes in shoes and clothing? Blunting of blades? Shoeing of horses?
In my BW game there is a Resources mechanic. That game is about (among other things) gritty survival.
In my Cortex+ Heroic game, there is no wealth mechanic. That is a game about vikings trying to find out why there are strange portents from the spirits of the wood and in the Northern Lights. Wealth is largely irrelevant. When one of the PCs robbed the drow of their gold, he earned a persistent d8 Back of Gold asset. There is no need for a special mechanic to track that.
Meeting a friendly border guard or pleasant fellow travellers is interesting, no doubt there; and if people want to RP that I'm all in. But, the chances of such RP generating any mechanical changes to the PCs are extremely low. Ditto for all the RP the characters would also likely do with each other during this time; the romances*, the minor arguments, etc.
Combat and risk and danger, on the other hand, have a quite decent chance of generating mechanical changes - lost gear or wealth, major injuries, death, getting separated, etc. - and that's what I-as-DM need to know about: how has the party that left Washington changed or been changed by the time it gets to Tokyo. (and there's always the very tiny chance of a TPK meaning they never reach Tokyo at all)
Let's just start with one assumption: that social interaction won't change the party.
That is already so far removed from my RPGing experience that it's hard to know what to do with the rest of what you say.
In the real world, people travel from A to B and survive; even flourish! In fantasy fiction, people travel from A to B without dying or being maimed along the way. (Conan does a fair bit of it, for instance; so do the protagonists in LotR.)
If you want to play a RPG in which more time is spent worrying about random encounters with jermlaine than finding out whether or not the PCs can keep their promise to the dwarves to help them with the giants, well, no one's stopping you. But that sort of focus is not inherent in the idea of RPGing.
Why not give them both opportunities - the journey, and the events after they arrive?
The answer to this is simple: if everyone wants to play an encounter with giants, why would we bother spending time on a trip through the Underdark? (Or from DC to Tokyo. Or whatver.) If you like that stuff, then good for you - knock yourself out! But if the players want to go to where the giants are, then a quick narration is fine.
'Dead' or 'diseased' or 'separated from the group and lost' or 'down some significant gear including magic items' are more what I'd be checking for after a long Underdark journey
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'Down a healing surge' conveys nothing more to me than I didn't get a good night's sleep. It completely trivializes the risks and dangers of such a journey.
And you know this because . . .? What level are these PCs? How powerful are their healers? What other magic are they using? How heroic are the martial characters? And how long is it since they took an extended rest?
Aragorn didn't become dead, diseased or lost travelling through Moria. Nor did Pippin.
The original Underdark module, D1-D3, doesn't imply that the PCs will become dead, diseased or lost travelling from the fire giant dungeon to the Vault of the Drow.
There's so much assumption and projection in these comments, that they're very hard to take seriously as analysis of gaming techniques.
But do you ever tell them these wild tales?
irrelevant stuff is only irrelevant until it becomes relevant, and without it the scope of the 'world' is limited to only that which the PCs are directly interacting with.
Like I said to [MENTION=23751]Maxperson[/MENTION], this is all just nonsense. I posted, upthread, an actual play account of the session in my main 4e game where the PCs were in the mausoleum of the Raven Queen. At one point, one of them had a vision of the tarrasque breaking out of the earth onto the surface of the world.
In my Dark Sun game, the opening scene took place in an arena, where the crowd were responding to news of the death of the Sorcerer-King of Tyr.
Just a handful of posts upthread, I posted an account of how the PCs in my BW game, while living in a tower in the Abor-Alz, heard tales of happenings in Hardby and in Urnst.
The PCs are not directly interacting with the tarrasque, or the Sorcerer-King and his assassins, or Hardby, or Urnst, and yet these things figure as part of the shared fiction!
And once you do, those rumours could instantly become adventure hooks!
In a player-driven game the players hook the GM, not vice versa.