Not convinced that taper bores due to boring bar spring is a complete myth.
Given the basic quality, age and less than stellar condition of lathes commonly affordable by relative beginners in the past its pretty certain that bed wear would be greater near the chuck. Flat edge beds, whether dovetail or Myford style, generate greater inaccuracy for any given amount of wear than the prism guide style used on professional machines. They are also harder to set just so for best results on a worn bed. Setting involves a few tricks too which are not as commonly promulgated as they should be.
Hence I find it reasonable to suppose that cutting forces could deflect things a bit as the saddle moves over the worn area.
Especially if there are various infelicities in the tooling such as imperfect shape, inadequate sharpness or errors in the height of the cutting edge creating excessive push out forces.
Most especially where relatively small bores are concerned boring tools need deceptively large amounts of heel clearance. I've more than once been too casual about shapes in the past and found that the cut was being made by the heel rather than the tip.
Even if the heel isn't actually cutting it can drag on the newly bored surface slowly forcing the tip out of cut as the bore gets deeper. Instant taper.
Something I've actually deliberately worked through in the past either to keep a stronger tool or because I didn't want to modify the one I had to hand which was fine for the finish cuts. Just not enough clearance for the first few cuts from the starter hole. So long as the last cut is right it matters little what goes on before.
I have a printed out, pictorial, crib sheet to remind me of heel clearance angles for smaller bores.
Obviously the cutting tip needs to be on centre and the lead in angles such that cut forces don't tend to draw the tool into cut or push it out of cut. Again with slender boring tools in small bores getting the shape and sharpness right so it behaves itself with a proper cut is important.
Mucking about rubbing a couple of tenths off each pass is not the way to go. Even razor sharp tools rarely behave themselves on hair fine cuts. I reckon that anything under 10 thou cut is asking for trouble due to the inevitable limitations of hand ground and honed tooling made by relatively inexperienced folk with relatively limited facilities. My experience is that a misbehaving tool tends to make a measurable taper.
The cure is to sharpen the thing properly rather than assume it was ok last time. I usually get bitten by one dragged out of the back of the tooling drawer for a special job that none of the general use collection can handle. Generally on a quick "Can you sort this?" job I don't want to do but can't politely turn down. Hurry-up and don't wanna are a potent combination.
It all gets much easier once up in the 16 mm – 3/4" (ish) bar size range. Even then excess stick out is a gremlin magnet. I've worked at 10 times diameter (and more) stick out when needs must but keeping under 5 times is far more restful.
As Geo. H Thomas was wont to say the common "mutant golf club" boring tool is something of an abomination. Expecting a neophyte to get good results from one is asking a lot. Quite apart from mechanical limitations getting a well shaped, sharp tip is hard. If only because of the difficulty of holding it up to the grinding wheel at the correct angles on the normal toolrest. My preference in smaller sizes is to use round HSS held at a slight angle to the lathe axis so you don't need to grind a neck behind the tip. take off just enough to give heel and to clearance with a short cutting edge.
Clive