"Commercials appear to override empathy"

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BMI would seem to be fine if you are happy to be treated like a number on a conveyor belt.

There seems little empathy or help for a patients with significant anxiety, which takes time and resources which costs money.

In this situation you are far better to wait if you can which will probably be longer, for an NHS operation at a normal hospital where they are much more empathetic and accommodating. So in summary if its speed then BMI wins but if you have significant anxiety don't expect BMI to do much to help you with this.