Well IMO, because Qatar was not a developed country around 50 years ago. And sure it was hard to find water here before they found black gold and became rich country. If you do not get water easily you have to spend it conservatively which makes it hard to build a Turkish Bath.

For today? Hmm maybe they are caring about Far East massage? Actually some hotels would have this facility but I have never heard any of them having Turkish Hamam.

BTW it is nice that you know the exact word used for Turkish Bath which we call as Hamam :). In Egypt when you say Hammam they were understanding stuffed pigeon as a meal.