There was discussion about hemophlia by the 1890s within the family.
QV wrote to VMH about a possible match between Maud & Ernie but then worried that Maud could be a carrier. Obviously it wasn't known yet that Maud couldn't be (at least through the QV link) but she was worried about Maud's general weak health and the first cousin connection. It's ironic that she didn't worry about this when promoting the Alix/Eddy match when the circumstances were similar and Alix had a chance of being a carrier due to Frittie's condition as well as Irene's son Waldemar. Henry Jr was born (and died) before Alexei was born (both in 1904 so perhaps not the death) but after Alix & Nicholas married.
I believe I did read that AIII & MF had concerns regarding the hemophilia issue as well as the general health of Alix. Mostly though it seems that they just didn't care much for her. She didn't make a favorable impression on her visits to see Ella and at other gatherings. Plus she wasn't considered English but German and, despite the Hesse/Romanov as well as the Hesse/Danish connection, MF did not care for Germans. Also the religious issue. MF had been in Russia long enough to know the importance of this and with Alix so unwilling to convert, she couldn't have foreseen that Alix would later become very devout. QA apparently disliked the potential match with Eddy for much the same reasons--German, personality, etc... I'm sure the 2 sisters consulted each other.
As for any rolling of the dice, that's true to an extent. I think it's true for anyone who carries a hereditary disease. Even today with great medical technology, there are some diseases passed on to children that are fatal. Anyone looking to marry and have children are faced with the same choices. Alix & NII loved each other and took the chance. It ended badly but Alexei had a chance of not being infected--even Irene had a non-hemophiliac son. It wasn't a 100% guarantee. Plus the Romanovs fathered a great number of sons--Alix's troubles both with her pregnancies and NII fathering so many daughters couldn't have been foreseen. There was probably every reason to believe that even if a son had hemophilia, there would be other sons who were healthy. That might sound cold-blooded but the 'heir and a spare' applied for a reason. As was pointed out, MF lost 2 of her sons before Alexei was born--illnesses and accidents could strike at any time.
By 1905 when Ena married Alfonso of Spain it was certainly discussed. Later when hemophilia took such a toll on their family, Alfonso would bitterly complain that he had been 'deceived' whereas in reality he had been informed that Ena's brother Leopold was a hemophiliac and took the chance. He chose to believe that because Ena had 2 other brothers and looked the picture of health that all would be fine. He had an even more important need for a son. NII at least had 2 brothers (at least until 1899) who could inherit and numerous cousins (like them or not). If AXIII died without a male heir, the throne would go to another branch of the family.
Alexandra would have good reasons to keep Alexei's illness a secret. One was the superstitious nature of Russia. She had always been regarded with some suspicion after she arrived in Russia 'behind a coffin'. As Ena (who also married into a very religious, superstitious country) found out, all kinds of rumors could start. In Spain it was rumored that a soldier had to be sacrificed each day so that his blood could be given to the Prince of the Asturias. Also, and going back to the original topic, AF was surrounded by enemies. If I had so personal a torment, I wouldn't want people who hated me to know about it. HOw much sympathy would she have gotten? If just would've been more for them to chew on--look AF can't produce a son, look she finally does and he's 'deficient', AF is such a bad Empress and now she's fallen down on her primary duty. Miechen would've started planning Kyril's succession then and there--Michael nonwithstanding. As suspcious as she was, AF could very well have figured Alexei's life may be in danger of ambitious relatives.