Oh sure, I thought you meant that.
Actually the slight inharmonicity of the overtones (we can't say 'harmonics' here
) makes a string more interesting (like contradictory spices in food), but of course an excess of that leads to problems, and in extreme cases even to difficulties to ascertain the pitch. The most infamous example are stiff thick nylon g-strings. But this stiffness seems to be really a complex variable depending on many factors in the chemistry (of plain strings) and on winding procedures of wound strings.
BTW the so called harmonics also do not fit into tempered scales, and that makes rich sounding guitars so much more difficult to tune than dull (fundamental frequencies oriented) sounding ones.
I cant remember who, but somebody here on the forum argued that this lateral stiffness doesn't come strongly into play for the question of effort of pressing a string because the actual sidewards bending of the string is not so big. I don't know, one would have to come up with some kind of measurement device for that...
As I already wrote, the real marvel here is that the same string set
can feel so different on two guitars of basically same geometrical properties (scale length, action) and brought to same tuning.
Music is a big continent with different landscapes and corners. Some of them I do visit frequently, some from time to time and some I know from hearsay only ...