Usually it's to remove constrictions, which is essential to cast bullet accuracy. A bonus is much easier cleaning. Done properly, it does not remove more than a ten thousandth at the muzzle and maybe three at the breech, and it moves the throat forward only about one thousandth.
My first Garand's original military barrel fouled so badly that its accuracy deteriorated before I could complete a match with it. Firelapping reduced cleaning effort by a factor of 6 (based on patch count), and so reduced fouling by a similar amount. The accuracy remained good through a match after that and clean up became a short job rather than all evening with patch after patch of copper solvent.
The Wheeler kit is a low grade knock-off of the Neco kit. Wheeler openly violated Neco's patent. The Wheeler owner, being an attorney, threatened to keep Neco tied up in court until it wasn't cost effective to keep fighting to protect the patent, so Neco gave up.
Where the Neco kit uses lab grade abrasives to speed cutting and limit particle diameter distribution, the Wheeler kit uses standard grade abrasive. The Wheeler instructions illustrate a barrel with toolmarks left at the inside corners of the lands and claim that is a correctly lapped bore. It is not. As a result, I have little faith that they understand the process.
The bullets normally used in firelapping, whether it's the Neco-type multi-grade process or a single grade process like LBT or Beartooth sell, are usually cast bullets. The principle is to pass a bullet lap through constrictions that will act harder on the constrictions than on wider places. If the bullet is too hard it tends to spring out and rub wide and narrow places equally. If the bullet is too soft, the firing pressure bumps it up after passing through constrictions with the same result.
Over a lot of experimentation, it is generally agreed by all the fire lapping proponents that a bullet cast to about BHN 11 is the best hardness compromise. That is wheel weights plus 2% tin or else 16:1 lead:tin alloy. Neco sold correctly cast firelapping bullets, though I only see their pre-embedded kits up on their site now. Their page used to have both, but the embedded type is repeated, so you'd have to call and ask if that's a web site error and if the bullets are still available?
The correct charges for the cast bullets are low. For the .243, about 5 grains of Bullseye should be good.
The Tubb Final Finish system is not a firelapping system. It is a polishing system. It runs long jacketed bullets at full starting loads. The bullets are intentionally bumped up to bear against all parts of the bore evenly, as it is not intended to be a constriction remover. Tubb uses it on his custom lapped barrels (which have no constrictions) to extend the throat life by cleaning up heat stress cracks. It will make a barrel easier to clean, like firelapping, but will not straighten it or remove constrictions.
Two more questions, If a rifle is getting 1/2 moa at 100 yds, and is capable probably of doing better, could there still be a need to fire-lap? Why isn't this done as a final step at the factory?