All wind instruments and all bowed string instruments produce a perfect harmonic series while emitting a steady tone. The most important difference between timbres of different instruments is in the attack, where inharmonic tones are also generated. Several old synths used this principle to greatly increase realism, by adding brief samples of attack transients to traditional subtractive synthesis, e.g.:

https://en.wikipedia.org/wiki/Linear_arithmetic_synthesis

Hmmm... was 'tone' a pun?

Why mention a strings 'slow attack' as less of a problem? No isolation software considers this an easy route.

Vocals are more effectively isolated by virtue of the fact they are unique sounding. Strings (and other sounds) are the similar in some ways but far more generic. All software out there indicates this, including the examples mentioned.

There is one important difference between the harmonics of string and wind instruments: it's possible to build a wind instrument that suppresses (although not entirely eliminates) the even harmonics, e.g. a stopped organ pipe. If it sounds like a filtered square wave it's definitely a wind instrument. But if it sounds like a filtered sawtooth wave it could be either.