I just did a flat with the bonnet method, quite long pile. I did think "this needs HWE" however I was amazed with the results it took about an hour and was nearly dry when I left. However if I could have I would have extracted it and I'm sure If I went back and extracted it now I would have dirty water. But its what the custy wanted!
I think I will always prefer HWE as it is the ONLY method which extracts the soils out of the carpet, however all the other methods have their place, the key is to have all the tools available. The ultimate method IMO is HWE with a bonnet afterwards.