Acid fluxes as used for plumbing contains mineral acids, or zinc chloride (aka 'killed spirits of salt'). They are significantly corrosive as are their residue, and are only acceptable for plumbing because acid residue inside the pipe gets washed away, and nearly all the exterior residue will be wiped off, leaving so little relative to the copper thickness that corrosion damage will be insignificant for many decades. If you loose 0.1mm copper from the outside of a plumbing joint, it doesn't matter, but the same loss from the strands of most finer stranded wire will totally eradicate them.
The residue of rosin R, RMA and most RA fluxes, unless badly burnt, is solid and reasonably inert at near-ambient temperatures. Therefore any trace organic acids it contains are 'locked up' and it doesn't cause significant corrosion if not removed, so it doesn't matter if its wicked up the wire under its outer insulation.
The only thing saving Frogblender's wire from rapid corrosion failure is the enamel on the strands. If its micro-cracked, it may still fail under the outer jacket, or the acid residue may re-mobilise due to humidity (Zinc chloride is hygroscopic and disproportionates releasing hydrochloric acid) and corrode through the strands where the enamel ends next to the solder joint.
For the aspirin technique any reinforcing strands should be removed first, before twisting the magnet wire strands (in groups per colour if its a multi-core in single jacket wire). You do *NOT* want an unholy mess of melted plastic and burnt aspirin left in the core of the wire, especially if you are preparing it for solder-cup terminals. Depending on the reinforcement fibre, fanning the strands and briefly flaming them to burn back the reinforcement may do the job, or you may have to separate and snip them with really sharp small scissors. Dip the twisted wire end in acid free halide free rosin paste flux, then press into the aspirin with a rolling motion with a solder-loaded hot bit. Once evenly tinned, clean with IPA on a lint free wipe. If you start close to the end of the wire, once the aspirin has broken through the enamel, one can usually get the tinning to progress up the wire to the length required just with flux, without further use of the aspirin, which eases cleanup.