Lady Magister Mathilde should not be used as a yard stick for the Grey College's modus operandi in regards to it's members. The only reason we didn't get a regular journeying is the Conspiracy. And the reason we didn't get put on a leash and orders to go investigate things or slip undercover is that the Sylvanian Campaign bought enough goodwill and trust. The College keeps tabs on it's graduate because Ulgu has massive potential to be abused, and with that may come limits on what she can or can't do.
And being a wizard comes with baggage. Being a Grey Wizard on top that comes with additional distrust, which will likely prove detrimental to making connections and deals. It's Eike's inheritance and she'll most likely end up in charge, but I don't see any reason to saddle her with additional baggage.