Why does the trip down the barrel not correct/cancel out the runout?
Because the bullet will engrave off center and will continue down the rifling this way. If the bullet somehow could right itself, it would need to tear away from the rifling. This is not going to happen with a jacketed bullet.
When released at the muzzle, the bullet will rotate with the tip out of true.
Some bullets can tolerate this and settle down. Others will not. Also, if a bullet is not flying true and has a wobble, how much more drag does this cause during flight?
How does this change in drag affect its flight path?
Like a poorly thrown football, there are limits to how much wobble the ball can absorb before its flight goes completely wonky. For best accuracy and distance, a true spiral on the football yields the best results.
The best way to test what your bullet will or will not do is to shoot it at the furthest distances you want. Small errors at 100yds, can be huge problems at longer distances. 1000yds is very unforgiving.
As to runout of the press, I doubt that will be the case unless the ram is seriously wonky and pulling the case sideways. Unfortunately, some offshored presses are showing this problem.
Where I have found runout has been in the sizing and seater die.
For the sizer, too much sizing can cause seating to go wonky even though the exterior of the neck is true - don't ask, cause I have no clue how this is possible but the runout guage is indicating this and has been repeatable.
Necks can be pulled out of true by an expander ball that is not coming out of the neck true. This one is easy to see on the runout gauge. Measure before and after. I have had a few FL dies that didn't have a problem and others that did.
Finally, the seater is the most likely cause of runout either by not supporting the case enough and/or a mismatch between the seating stem and the bullet ogive and tip.
So to test your gear, measure the runout at each step of reloading and you will quickly identify trouble areas.
You don't need mega dollar reloading gear although it can help. BUT invest in a quality runout guage cause even big dollar stuff may not be working well with your series of components.
Better neck sizing dies like the Lee collet die and various bushing dies seem to get the job done without creating any runout. I feel 2 thou neck tension is plenty for match ammo. Some will use alot less.
Couple this with a Redding body die and the case can be sized without issue.
The Forster and Redding inline seaters seem to be the most successful in seating VLD bullets without creating runout. Reg. seaters are hit and miss and random - again, measure to find out.
Does alot of runout really cause problems? I have had ammo with alot of runout shoot some very decent groups but the averages were not as good as ammo with min runout.
With the amount of fuss and effort we put into making precision ammo (1/4 min or less capable), why settle for ammo with high amounts of runout ?
There are many areas in precision reloading that really don't affect groups 'MUCH' but that little bit less precision is what we spend all our efforts trying to eliminate.
YMMV.
Jerry