You are being ignorant of the probability of being charged and actually sentenced to the crime. While the punishment is harsh as a deterrent, you need to have 4 religous, sane and righteous men with good conduct to testify that they explicitly saw with their own eyes two people of the same sex having intercourse. Now where are you going to find that? You're going to have 4 of these good men peeking into people's bedrooms or what? It's almost impossible to convict someone, unless they confess themselves. They cannot be forced into confessing anything, and they will have to testify against themselves four times - each time, the judge will tell them to SAY NO because if they say they didn't do it and it cannot be proven, they cannot be punished. If they are drunk or insane then they cannot confess against themselves. Alan Turing simply would not have been convicted if he was under Islamic Rule, unlike British rule where he was forced to confess.

Moreover, there is no exact punishment for homosexuality in Islam. The are currently mroe than 50 Muslim majority countries with varying degrees of sharia law. Of those, the only countries which have a prescribed death penalty for homosexuality are:
Mauritania
Somaliland (part of Somalia)
Saudi Arabia
Yemen
Iran

The United Arab Emirates also has, legally, a death penalty for acts of homosexuality. However, most cases are dealt with via fines, prison sentences, or expulsion from the country. I have not been able to find any cases of a death sentence having been dispensed by the courts in the United Arab Emirates.