Anyone who says FIS isnt of any value has limited experience.
You're not doubting the experience level of the OPs instructor, are you?
A FIS can be very useful, especially if you do long flights over potentially harmful terrain, need information on conditions ahead, yadiyadiya.
But the way I read the original post is that somebody was having a flight lesson, most likely returning to the departure airfield in about half an hours to an hours time, doing some general flying about in the local area while doing the exercises that each of us have to go through. Obviously one of the options is to change frequencies and ask for a FIS, or remain on the tower/AFIS/AG frequency and monitor what's happening there.
As far as I'm concerned, if you're staying close, it makes far more sense to remain on the local frequency and monitor what happens there. You'll hear all inbound and outbound traffic, and learn of any changes happening to your specific destination, up to runway changes, QNH changes and everything. Without even asking. Most likely, since it's both your departure and destination airfield, ATC (if any) will keep your details on file anyway, and will know the general area where you'll be flying, so even if there's an emergency, they are probably as good, or even better, than a FIS from a unit 100 miles away.
Frequency change approved means just that: you are allowed to change frequency, but you don't have to. Depending on your intentions, you might want to stay on frequency, shut down the radio altogether, or switch to another frequency. Whatever you do depends on a number of factors, one being how far and how long you're going to be away, the other what level of service you can realistically expect from the unit that would be providing your FIS, at the place and altitude you're going to be operating.