if it dosen't work I'll use their resistance against them and transition into another technique.
This is what I consider to be the real concept of Aikido, the ability to be able to rapidly switch from one technique to another and take the opponents balance. If a person trains in the manner you mentioned and highly refines his/her ability to take the other person's balance as soon as the opening is created, that's what I consider advanced Aikido.
I train in Aikikai, which to most may be the softest of Aikido lines, and have been fortunate enough to have a great sensei who has made the study of this art his life. The great thing about it is that he shows you how/why it works, and even if we performed the technique sloppy and it worked we are to do it over again and again with proper technique, and thats what matters. No matter how resistant or strong the opponent maybe the stress put on the joints from such behaviour will result in a break or just a clumsy fall. Now I understand many don't teach this why perhaps that is why it is dogged so often.
Here something I found interesting, note what he says was the result of the perp resisting =]
Goal:Enshin Honbu Dojo