Are the items in newbie "kits" actually used during or after training?
Well going by Sportys own price lists

Flight Gear HP Crosswind bag - 50
PHAK - 16
AFH - 16
AWTB - 16
FAR/AIM - 16
Fuel tester - 11
E6B - 40
Logbook - 16
Plotter - 16
Private Pilot Maneuvers Guide - 16  

TOTAL: 213

If the list price is 150, that represents a savings of 63.

Of all that equipment, save for the maneuvers guide, you will need the rest of it to complete your training knowledge test and checkride.  The E6B and the chart plotter are a little anachronistic these days but can still be put to good use for time or fuel sensitive flights.   You will make good use of the flight bag for the rest of your flying career.  All in all it’s a pretty good kit. 

One thing they left out and I highly advise you buy is a flashlight and spare batteries.  It’s a $30 item and it could save your life if you ever have an electrical failure at night.  I would recommend the Smith and Wesson Captain’s Flashlight for this.  Avoid tactical flashlights with high output white lights; these are counterproductive when flying and will wreck your night vision.  Another good option are the head mounted lights popular with cavers and climber.  Select one with white/red output and, again, not too bright.

Another useful item is a headset.  High end ANR headsets cost over 1000 USD but ther are economical and good quality one in the 200-300 USD range.  I used the David Clark H10 series headset during my primary flight training and still have the headset handy for passengers.

I would recommend spending the money on the following apps

Either ForeFlight or Garmin Pilot as an EFB.  Best thing since sliced bread for charts, maps, weather products, flight planning, filing, etc.  much lighter and a hell of a lot cheaper than paper products for this.

ASAs FAR/AIM - Heck of a lot lighter than a paper FAR/AIM, can search regulations faster and it automatically updates annually, instead of having to buy a new paper one every year.