As noted in the comments, it is difficult to make this intuitive idea mathematically precise. In practice, even slip knots get stuck on themselves when pulled tight.
One may look for monotonic ways of untying an unknot. Holding a long unknot and pulling on the ends, one may expect for example that the number of maxima with respect to direction between the ends does not increase. Otal proved that one may always undo an unknot without increasing the number of maxima, so there is no obstruction of this type (he works with closed knots, but I think the proof should work for long unknots, ie unknotted strings/1-tangles). Dynnikov proved that one may monotonically simplify a (closed) unknot in grid position /arc diagram, but it’s hard to see how this might translate into something physical by pulling both ends of a long unknot.
