Medically necessary circumcision
Finding an answer to that question is complicated by the fact that the medical fraternity in many nations have been unwilling to consider alternatives and that stretching the foreskin early can cause problems which are then used as a justification for circumcision. We know that upwards of 95% of cases of phimosis can be treated with topical steroidal cream and stretching exercises, correcting in only a few weeks. Various other non-surgical treatments exist and if those fails there are even surgical procedures less invasive then circumcision such as the 'dorsal slit'. What we can say is that after considering all the surgical and non-surgical alternatives a case where circumcision is truly necessary should be extremely rare today. Advances in medical science should make it rarer still in the future.
in the study below you can see that many nations report a circumcision rate of 0.1% or one in 1000 men. Notably, these nations represent populations from a diverse range of ethnicities which may rule out variance among ethnicities. Given that these nations will still have populations that engage in routine infant circumcision and that they may not be using all available alternatives this number may represent an upper bound on the proportion of men that actually need to be circumcised. I propose therefore that less than one man in 1000 will need to be circumcised given current medical knowledge and that the rate may be significantly lower than that. [1]
The Finnish National Board of Health found in the 1970s that 0.023% of men over 15 required treatment for phimosis or paraphimosis. Even if we assume that all of them required circumcision this is still an extraordinarily low rate, and it is likely that only a proportion of them required circumcision.[2]