Although Alix wanted her daughters to marry for love, it seems she wasn't open to marrying them off to men who were not of noble birth, so, (had they lived) it's possible that whether she and her daughters like it or not, OTMA would have to marry a prince or anyone noble, and necessarily would have to live wherever that man would be. Their ranks truly makes it complicated for them, and it would be likely any (or all of them) would follow the example of their Aunt Olga and lose their title (which is anyway not a big deal for them). Having said that, I think Anastasia would steadfastly oppose that idea of being married to an English (nobleman), and would do everything to avoid suffering a fate of being stuck in a 'marriage of convenience' plus living thousands of miles away from home ~
You are right - Alix didn't want it because of those tensions ^^ According to the book, she said that at the time the family were already imprisoned in Tsarskoe Selo.
Btw...
I found one of Vera Konstantinovna's memoirs but it's entirely about her family. I found curious similarities between Igor and Anastasia.
Vera described Igor as 'always lively, funny, witty and ready for mischief.' She also said he nearly drowned (in the Masurian marshes) during WWI; Anastasia also almost got drowned (can't recall where) before, but it happened when she was younger. XD, what a coincidence!