Is there a point to gaining "Connected:" quality after a certain point?

There's an opportunity card that crops up when you have both Connected: The Widow 30 and Favors: The Docks x 5, called "The Acacia and the Butterfly". Using that card will cash in one connection or the other for rewards. (i.e., it costs 465 change points of Connected: The Widow (which is what it takes to get Connected: The Widow 30) or Favors: The Docks x 5.)

If you'd like to raise your Connected: The Widow without working for her directly, there's another opportunity card that will let you increase your Connected: The Widow or Connected: Urchins a fair bit, as long as you have at least 5 of each connection: "A familiar face by the school railings." This will let you trade 15 change points of Urchins for 30 change points of The Widow, or vice versa: using that card repeatedly (when you can find it) is a quick way to raise both connections.

On a bit of a tangent: the Connected qualities are being migrated over to a different system: Favors and Renown. Renown is how well-known you are with a group (equivalent to "you must have X Connected: Y to take this action"), while Favors (capped at 7) is how much you can induce that group to act for you (equivalent to "you must spend X Connected: Y to do this action"). The migration is happening pretty slowly: it was promised as of August 2015, and as of May 2016, only four factions have been migrated.

When the migration to Favors/Renown happens, your current Connected quality will be cashed in. You'll get a maximum of 7 Favors for that faction, and a maximum of 50 Renown (soft-capped by the requirements to raise it). But that's a fairly paltry payment, as things go, so you'll probably be happier exploring other parts of Fallen London rather than grinding the Widow purely for the (very) eventual switch to Favors/Renown.