I think that logic fails for two reasons.
First, if you’ve never visited Vulcan, and you meet a Vulcan on the Stair, you don’t know what he’s saying even if you are both Wardens, as it is unlikely both Wardens have used the Door to Vulcan. I don’t think that is intended. Worse, if neither of you arrive back on Vulcan by Door (for whatever odd reason) you still can’t understand each other.
Secondly, imagine a thousand languages being spoken in the Stair. But wait, there are merchants and cargo handlers and all sorts who don’t have Warden skills. And if your Warden hasen’t been to their Door, you can’t give them instructions? Even worse, your labor help may not be able to talk to each other. And there are plenty of game stories where not everyone (or every PC) has exegesis. You may have a PC based only on sorcery or Eidolon, so the Warden has to do the translations.
I suggest a small fix that meets the intention of the rule set.
The rule is better if you just say:
Once attuned to the Grand Stair, ie, Warden, you understand any language that exists paired to a functioning Door— or in a polycultural gossamer, all native languages of that world.
A particular GM could wrinkle this by saying the further you are from the transmitting Door source, the less likely the translation works. The key to that particular complication would be narrative emphasis (mostly mine) that the Infinite Stair is very very big and you can run across people that are so far out of your region of Stair you cannot talk to them— or not talk to them well.
Kill all doors to a gossamer language source and the understanding vanishes, as it is no longer transmitted to all Wardens. Destroy a world and the language is gone as well.
If a language vanishes, someone needs to go find out what is going on!
Talk to your GM in session zero before the game starts about the baseline of such powers in play.