Former New Yorker here who had a great familiarity with the WTC complex; I passed through it daily on my way to work elsewhere downtown for 5 years. It seems almost impossible to me for one tower to collapse without affecting the structural integrity of the other tower. They weren't that far apart physically and were connected by a vast underground complex of shops, mechanical components, parking, subway stations, etc.
If, by some miracle, one tower collapsed and the other remained intact and structurally sound or at least stable enough to be repaired, it would have been unusable for some time. The subway lines would have been affected (part of the underground complex connecting them) and the sheer amount of debris nearby would have required removal before the surviving building was usable. This task, due in part to the presence of human remains, took quite a bit of time.
Bearing in mind that these two buildings were connected underground, it is also possible that debris removal of the collapsed tower would have of necessity compromised the structural integrity of the other. Dismantling one tower would have been an immense engineering challenge and may well have taken years. Due to density, demolition would not have been a safe option.