Have we become so lazy that running for a minute or two from the outpost in zone 1 to a place we want to go in zone 2 is that much of an issue?
It's not really a matter of being lazy; it's more a matter of convenience. Since you would be paying in tabs, you would still be "paying your dues" to use the process, but it would be quicker than "Repatriation + outpost warp + hoofin' it."
For fairness's sake, possibly only allowing said quest to be completed for zones (or surrounding zones) for which you've completed a supply run (a prerequisite of sorts), so that people couldn't literally "book it" from one nation to another unless they had the supply run of the starter area of said destination nation (lolrhyme) complete.
I for one actually enjoy the little walk instead of simply being placed at every convenient spot you would want to go to.
This would be another option for travel, just like chocobos, airships, current Repatriation, outpost warps, WHM teleports, BLM Warp/Warp II, runic portals, Kaduru-Haiduru and Shihu-Danhu warps in Aht Urhgan, Wildcat warps to Aht Urhgan, retrace, teleports for Allied Notes, or confluxes within Abyssea(that list may or may not be exhaustive lol). Note that none of those are mandatory--you can run from Bastok to Jeuno if you so choose; you can run to Mhaura and take the boat to Aht Urhgan if you so choose, likewise for teleports involving Allied Notes. As stated, it's a matter of (wholly optional) convenience at a cost for the sake of being convenient. Also of note is that it isn't a POS Hack, so you simply couldn't be placed at every convenient spot to which you would want to go. Since there are only a set number of spots in a zone you could go, and they are usually at the entrances of the zones themselves, some leg work is still necessary.
That all said and done, the only place not easily warped to (if you dont count Quifim's warp) is currently Jeuno. That would really be the only addition we'd need.
There's a book outside Jeuno in Sauromugue that would put you pretty close to Port (the book is at E-6), so the OP's idea would cover that so you wouldn't have to set your HP in Jeuno if you didn't want to do it.