I'm going to make a bold admission here. When I started teaching Tai Chi, I made similar claims to my students. These claims were largely based on the fact that I only saw my own teachers training methods. When I saw other styles, they were at competitions, where I could only observe the external sense of peoples forms. Combat was only within the severe restrictions of pushing hands competitions.
But as my experience of teaching grew, I began to comprehend other systems and styles. I began to recognise a core set of principles that they all adhered to. I had to swallow my pride and realise that there are quite a lot of good teachers - all patiently teaching valid systems.
Even within the same style, teachers repeat the same traditional practices - just calling them by different names. Take Silk Reeling (the traditional family name for fixed step Chen style movement training)- I have heard it called "Silk Winding", "Winding", "Reeling", "Powering in Circles", "Spiral Training" and "Silk Twining". There seem to be minor variations on elbow position, based on different practical applications, but the exercises are all the same.
There are many forms of tai chi that concentrate on the medical and spiritual aspects of tai chi quan. To reject these practices is to completely discount an important part of the martial journey. By all means, split the disciplines into different exercises, but don't reject them. A martial arts teacher should be able to enable their students to look after themselves martially, physically, mentally and spiritually. It is worth remembering that all Chinese martial arts came from the establishment of Zen buddhist and yogic practices in China.
As well as tai chi, my teacher taught me aspects of first aid, diet, cooking, meditation, business, etiquette, Buddhism, Chinese culture and history.
I understand that all professional Tai Chi teachers need to establish a unique selling prospect - or "marketing". But to do this at the expense of other valid lineages or by rejecting spiritual practices is at best a lack of understanding of how other systems work - and at worst, betrays a severe inferiority complex.