The Mewmans were winning the war, the problem is that Mewni was vastly outnumbered compared to monsters. Even though the wand could theoretically create infinite resources, it couldn't create infinite manpower, unlike monsters who can operate with human-wave tactics.
Consider how many children the Avarius family has, or how many Buff Babies there are. Now, consider that the majority of Mewmans have one or two children. Even though Butterfly Kingdom has a high, concentrated population, they're dramatically outnumbered.
By the time Solaria got assassinated, she was losing a war of attrition. If the Solarian Project had been perfected, and one Solarian was equal to X amount of monsters, then Solaria could have won, especially if she managed to figure out the Darkest Spell.
The fact remains, however, that none of the writers reduce Solaria's motivations to bigotry and hate for something different, rather than devotion and love for Mewni, and therefore make her literally Hitler instead of something inspirational. She was the only one in her entire dynasty to put Mewni before herself, and it's disgusting that people hate her.