Could Alix of Hesse have had a better time in Britain if she'd fallen for Eddy and married him than she did in Russia? She was shy and did prefer to remain at home with her family but the British Royal Family could spin that towards Alexandra being motherly and harken back to the Victorian family ideals.
Most likely yes. I'm not sure about Eddy, but none of Bertie's other kids were social butterflies. Britain had no history of religious mysticism, so no danger of her falling into that pitfall. Plus even if she intervened in politics she couldn't do much damage. They only issue would be a carrier of hemophilia marrying another potential carrier; though I don't think that any of Bertie's descendants showed signs of hemophilia, so maybe it wouldn't be a big deal.
Personally, I see this scenario a lot, and it is widely agreed that Philippe would not have accepted it. My question is, (since I don't think this question is ever brought up elsewhere) were there anyone else besides Alix of Hesse who would serve a better role as Empress?
Undoubtedly but I'm not sure who. Supposedly he had a flirtation with his cousin Victoria (Bertie and Alix's daughter) in 1883, so that's an option. Or her sister Maud, future Queen of Norway. Though both were his first cousins and the Orthodox Church forbid such unions, so I don't know if Alexander or Nicholas would try to overrule the ecclesiastical opposition or not. Then there's one of Wilhelm II's sisters, either Sophia or Margaret of Prussia. Not sure if the Romanovs would want such close ties to the Hohenzollerns and such a match would be disastrous for the Tsar if World War I still broke out. What about Elena of Montenegro? She's the right age, was already Orthodox and was educated in Saint Petersburg. Or one of her sisters. That's about all I got.