sound almost like acrophobia,look it up...let him have his own comfort zone...if you dont go to the gym or the bars and someone insist you go you will feel out of your comfort zone tooo.
Am I wrong to make him play? -- your question
No. But, by your own words, "it's the same process every year".
I feel that your son suffers from an anxiety "disorder" (probably social anxiety) which is different from being anxious or shy. Anxiety disorders affect the physical, emotional and mental aspects of a person and as thus, requires specialized help in learning how to "manage" one's fears/anxieties. First, I might suggest that you google the term "social anxiety and children" or "anxiety disorders in children" or "how to help a child with anxiety" or similar words/phrases. There's lots and lots of information on the internet, in bookstores and public library systems. But, most children require a personalized "plan" of action. What you are doing is called "desensitizing" and is one of the treatment processes for anxiety sufferers but it is only one; your son appears to require more help. By the way, most treatment plans for anxiety are multi-modal.
As always, the next step is to contact your family doctor re this issue. If he/she is unable to help you, then ask for a referral to a medical mental health specialist with experience in anxiety disorders. Don't be afraid; many of the sessions are few and short but you (the parents) will be given a "plan" or ideas on how best to help your son. He can't do it alone; he needs help in learning how to manage his fears/anxieties. If anxiety is the issue, I assure you that your son will not outgrow this nor will it go away. But, anxiety is highly treatable and the prognosis is excellent.
Our child was diagnosed with severe anxiety at six years of age and today is doing very, very well (she is now in high school). The path can be long but it gets easier. All the best ....