For reference, the Colossus of Rhodes (which I assume forms some kind of inspiration for the Titan) was about 100 feet tall. The Pharos, which was roughly contemporary, but a building rather than a statue, was about 450 feet, and was just about the tallest building in the world until it fell down (not counting the Great Pyramid). Before the introduction of modern building techniques with steel frames etc. the maximum height of a building seems to have been about 500-550 feet.

I'm not an engineer, but it looks like Shintouite, while a great building material, is kind of like a super-concrete: it has wonderful strength under compression, but probably not so much under tension, and thus buildings and structures built out of it might well be subject to the same sort of problems that limited height before the introduction of steel reinforcement. Most prominently, even minor earth tremors, and wind (in the sense of blowing it about, not eroding it), could wreak havoc on high structures built from it.