The relevance of using properly props (yoga strap, chairs, bolsters, cork blocks, and sometimes wall!) is mainly understood during your first Iyengar practice. I used to say, props are your "friends", they are here close to you to support you, gently, giving you the right angle in your personal alignment to release some place in your body where you are struggling and to focus some others area where you are totally absent, or running away from.
Props are there to guide your practice , to prevent your-self from neck, knees, hip injuries. Props are fundamental when your goal is to learn mindfully subtle transformation that will make you feel, think and be different within you and with others. Iyengar approach is made to teach and practice smartly to individuals with may have not evenly, the same strength and the same need in the same moment.
This is what we call customized teaching, each teaching, each practice are different but keep its foundation on a relevant frame chosen for a particular focus or needs. For example, if I want to work on "inversion" today to balance mood and energy level, I would then customized few variation for my body type, and prepare breathing exercice with by my side a timer to set in a posture for several minutes, then switching slowly to the next level and so on. For a single asana, this might take an hour....not 2 min as i witnessed so many times in "commercial" yoga studios. My goal is to embrace time and patience into my personal practice. This is how Iyengar inspire me.