Folks:
Gosh, lotsa stuff. With a thread like this you just have to use the mulligan stew approach...throw anything in and see how it boils.
Zeroth...note that I am not a professional electrician, and do not have the depth of experience that this job would provide. I do have about 10 years of adding to, replacing, and upgrading electrical systems on various old houses I, my family, and friends have owned to refer to, and I do grok the relevant parts of the NEC, even if I can't cite article and section. I find it quite disturbing that on 90% of the occasions when I recommend to various DIYers I meet at the stores that they go down to the nice library and ask the nice blue-haired ladies to point them to the NEC residential manual the reply is a shrug and a return to picking out 2 1/4" deep old-work boxes. Sigh.
First...there is a 10th circle of Hell for insurance company policymakers and their one-size-fits-all Stat 101 modeling methods. Each K&T system must be considered individually by a competent electrician, like any electrical system. An intact, properly loaded K&T system, all splices properly twisted and soldered, rubber and friction tape, and properly added to is quite safe. A poorly hacked system like my house used to have, with old-school NM twisted or simply hooked on to stripped NM, 6 cables jammed into inaccessible 3 1/4" round j-boxes, hospital grade electrical tape :), all buried in cellulose insulation, is unsafe...but quite insurable, since all the *visible* wiring was old NM. Old NM, some of it beginning to pyrolize in the hot, overstuffed boxes.
Note that the K&T insulation, not so overheated, was still in good condition, though 30 years older.
Second...metal does not "crystallize", but it does fatigue, leaving a rough, "crystalline" appearance. A "cold joint", where the solder was melted and did not heat the wire enough to bond to it, has a rough, "crystalline" appearance. A properly made solder joint does not rely on the lead for conduction, but twists the wires intimately together. The lead protects and secures the joint.
Third...wire nuts can fail, yes, but in modern systems they are all stuffed in (hopefully accessible) boxes. The nut, if put on right, also twists the wires together internally, as well as clamping them with spring pressure. I also like to wrap some tape clockwise around the skirt of the nut, which a lot of people seem to hate, but I have a delusion that it adds a slight margin of safety in case the spring should weaken or the shell should become brittle or otherwise lose its grip on the spring. I have found older (bakelite I think) and ceramic wire nuts that were only held on by the tape wrapping some paranoid electrician gave them, pulling quite easily off the still well-conducting twisted-together wires. Of course those were pretwisted, but I find that Ideal wirenuts are quite capable of internally twisting 2 or 3 wires. With most other
brands I usually pre-twist.
Now for the original post. If you're not planning to do a from-scratch rewire, it would probably be best not to change much, as long as the old system is safe. There's really no way to recommend what you'd do unless I saw the system in person. Perhaps as you rewire parts of the house for convenience or remodeling it would be a good time to rationalize some of the circuits, if there's more than 2 represented in each room. Having 2 feeding each room (each circuit itself going to several rooms) can be quite nice when one of them fails, and you don't have to drag out the candles. :)
Cordially yours: G P