Because they are quiet and fabulous and beautiful and smooth as silk. And they look like this-
bosporus ferry
I have never seen a "gay" hamam and if there is one, it's undercover and you won't find it. But if you want a great experience, go to the Cagaloğlu Hamami, which is this incredible 18th century hamam. It's all hot slabs of marble and domes and hairy massage guys and mounds of soap bubbles. It's an amazing experience and right in the core of the tourist area but frequented by the locals.
The Dolmabahçe Palace in Beyoğlu has the world's largest crystal chandelier and even features a Baccarat crystal staircase.
Well, IMO the two are equally amazing in different ways.
The Blue Mosque is all about light and soaring columns and that gorgeous Iznik tile and you are right about it's beauty.
Yet the more I see it, the more I love the dark and brooding architecture of St Sophia. It is what I'd expect to see in Middle Earth. Plus those mosaics are really beautiful and it is about a thousand years older. It was the largest church in the world for over 1,000 years and then, after the Conquest, it was the principle mosque of Istanbul for nearly 500 more years. It was the model for all the famous mosques of Islam. When you walk the halls of the Aya Sophia you are walking though perhaps the most important architectural treasure of the world.