In our classes,our sensei emphazises on teaching principles, body feeling and letting your energy blend and flow rather than a rigid technique for a whole lesson, especially in the beginners class. If people feel comfortable with their body and its specific natural movements and abilities and are able to use aikido's principles, they find it much more easy to learn a defined technique. Also, we do a lot of randori. It's amazing how often beginners discover many techniques by themselves just by applying the moving principles of aikido.
Our sensei's aikido is influenced by different styles, mainly by Shoji Nishio sensei. So we do a lot of "freestyle" or "hybrid" aikido, too and train specifically Nishio sensei's style before his seminars or exams.
So I don't think it's bad to allow some variation if you and your students feel more comfortable. It can be very fascinating.