Hi Larry,
You are right to have the tip of the Iron nice and clean but to have no solder on it may also present a problem overall. The need to heat up small joints and those on PCB is usually not a problem BUT the problems I have come up with is dealing with thick wires out in the cold or where the wire is thick enough to draw all the head from the iron. Also as Thermodynamics come into play with using a soldering iron, it is always good to have a clean tip but also one that has some lead on it to help aid in the interface from Iron to wire.
Now as to difficulty with thick speaker wires, it is best to have clean copper wire in opposed to that with a tarnished surface that resists solder sticking. If the tarnish is on there and the head can't get through it the a stainless wire brush would help in cleaning up the interface area and I have used solder flux in cases where it is almost a sure thing that the wire is going to be trouble. I came across this kind of thing in a machine shop where almost any wire stripped has oil or is tarnished. Then there is the heat transfer issue. If you are using a conical solder tip the soldering of the thick wire will require you to not use the tip of the iron but the thicker area midway up the tip to get a lot more heat transfer to accomplish the job. I have found that the further down the base of the tip towards the handle the much better teat transfer you get. In the case of very small digital transistors the same idea is used except that you want to use the tip to keep heat transfer to a minimum to avoid causing the failure of the component. And as all technicians in the past few years probably know, avoid the Lead free solder as it requires higher temperatures and takes a longer time to get the job done. goo think I bought a pile of Kester 44 some years back at $7.00 a roll as I have seen it as high as $32/ 1LB roll for the ,031 stuff.