She certainly was lovely and well-connected. It will never cease to amaze me, why her parents refused to let her find a marriage partner.
She had been 21, her elder sister Olga 23 and her younger sister Maria 19, all of them at a perfect age (at that time) to get married or at least engaged. Even Anastasia had been almost 17.
Married or at least engaged into a foreign monarchy would have saved their lives.
Tatiana had in fact a suitor Dimitri Yakovlevich Malama. He was a commoner, but obviously accepted by N and A. He later joined the White Army and was killed in action in 1919.
But I know what you mean. The Tsar's daughters certainly weren't short of candidates. I don't think their parents actively prevented any marriage. They just wanted them to marry for love and be happy.
Olga f. e. turned down the Crownprince of Romania, because she didn't want to leave Russia. Tatiana and the others had surely similar feelings.