Well, I think I can provide a Bulgaria perspective, though I don't claim it's the only possible one
Basically, it's not that implausible, under certain conditions. At the time Bulgarians had a mostly positive opinion of Romania, due to the Romanians helping liberate Bulgaria in the 1877-1878 war. So it could be done, especially as Romania was seen as a bulwark against Russia. This is of course why the Russophobic Bulgarian government at the time offered the crown to Carol.
As for the conditions, any attempt to dissolve the Bulgarian church and the Bulgarian government would be the best way to end this union really quickly. The only way it would work would be if Bulgaria retained most power over its internal affairs - something like Sweden-Norway.
And like the latter state, it would probably collapse when Romania would inevitably try to turn the Union into a centralized state.
As for why it didn't happen in OTL, it wasn't due to the opposition of the Great Powers, but due to the opposition of
a Great Power - Russia. At the time, Alexander III was determined to have control of Bulgaria, one way or another, and the Romanians didn't want to antagonize Russia. That's of course also why Ferdinand got chosen in the first place - nobody else wanted to risk the anger of Russia. There is possibly apocryphal story that the Bulgarian regent Stambolov was so desperate to get a prince that when he heard that there were some rather unsavory rumors about Ferdinand, he replied: "Bring him even if he has horns on his head!"