I can't attend my ESA assessment

If the assessment provider and the DWP have letters about medical conditions and the effects, they can do a paper based assessment. It is up to them whether they feel they have enough evidence to do a paper based assessment though. If your GP has provided a letter stating that he cannot travel and needs a home appointment that really should be enough for him to have one. I would phone the assessments provider and ask to speak to a manager or make an official complaint about the way he is being treated. You may even want to get the MP involved and I'm sure something would be done then. It appears to me to be quite clear from what you have said that he cannot possibly attend a clinic to be assessed so I really don't know what the problem is.
I assume the assessment provider is Capita, all their website says about this situation is:
It may be possible to have a home appointment dependent on the available Medical Evidence you have provided to support your claim. You may also need to send a letter from your GP supporting your request. For more information please contact Capita's Enquiry Centre on 0808 1788 114.
I would advise you to call them again, ask to speak to a manager and/or threaten them with MP involvement and, if you still don't get anywhere, contact the MP. Good luck!
Lee