Pourboy,
Looks like I got several people going on this. I appreciate you being first to take the ball and answer the question! While we're at it, just because I am new to the forum doesn't mean I am a "newbie". I have been in this from all angles for the past 40+ years as I said. I made my first bullet mould in 1959, and am currently modifying production moulds to hollowpoint if anyone is interested. But, back to the question.
I will never argue with anyone who believes anything helps to make shooting more accurate, fun, whatever. I do reserve the right to question if what works for you is, in fact, necessary or productive in a way such as we may generalize about. One of the above answers mentiones "springback". Certainly this is considered to be a problem, but consider two things which may contribute to this "problem". First, is the check shank properly sized for this brand of checks? Second, don't forget that the bullet and check are sized to an even greater degree by passage through the barrel! If the check is fully seated on the shank at the time of loading the pressure of firing will certainly force it firmly against the base of the bullet between the case mouth and the origin of rifling where it will be crimped firmly, again. You mention unexplained fliers, it is possible that if the check didn't fit the shank properly that the check may come off after the bullet leaves the barrel. Lyman in it's older books stated the belief that if the check came off after barrel exit that it had done it's job and this was not a problem. I think all of you will agree that if this happens it can cause accuracy problems which would be totally random.
This is not directed by anyone in particular, but while we are about it there is a word which I have seen used incorrectly in every cast bullet article and in every publication gun related. That word is OBTURATE! A bullet expanding under pressure to fit the bore of a gun is NOT OBTURATING! Call it what you want, bumping slugging, whatever, but the RESULT of these is OBTURATION, a sealing up or closing. This is the way it is defined in Webster (the dictionary) and used in reference to artillery. To be accurate, in every cartridge firearm the cartridge case is an obturator, which, coincidentally, it does by expanding under pressure.
This is for everyone. In your answer you mentioned several things which you believed that annealing of the gas check improved or covered for. The first was raised sprues. That should be corrected by your casting technique wnd can be caused by improperly striking off the sprue, allowing the bullet to cool to too hard a state, or if you are using a eutectic alloy which has very little of a moderately soft state between the liquidus and solidus. There are too many references to mention, but start with the Lyman Handbook of Cast Bullets.
Concerning annealing letting the check stretch to accommodate a too large check shank, is this real or is your sizing die starting to crimp the check before it is fully seated? Either can obviously the case. Using a "gas check seater" on Lyman, RCBS, or Saeco sizers may help here. Over the years I have encountered the same problems and have resolved them by casting and check seating technique.
You and all others on this forum may be aware of the following, but, for those who are not I would like to mention some articles which may be helpful. These are: "Concentric Lubri-sizing" by Ed Wosika posted on Sixgunner.com/guest speakers. The second is also by d Wosika and is on the Hanned Line web site, Hanned.com and is titled "Lubri-sizer Sizing Dies Technotes". The last describes a source and a modification to production sizing dies which avoids the pre-mature crimping problem and assists in concentric sizing of the bullet.
Just to help establish my bonafides, I have been able to get a .35 Remington at just 2'' at 200 yds. with a cast bullet (RCBS .35-200GC) as well as two of my Marlins in the 1" area at 100 yds (Lyman 429421, what else?). Lube was NRA. I must be doing something right, except for selling both of these rifles. Their replacements have been OK, but not quite so good! (They doubted Elmer too, FWIW)
Finally, again for everyone, if annealing gaschecks works for you, by all means continue. I have doubts that the result can be as consistent as the checks are when received. The above groups, which were repeated more than once, were with Hornady checks used as received. Sorry for the length. This one I'll leave alone after this!!