And maybe this is late, but considering how long Prince Richard, the sole surviving son of Prince Henry, younger brother to King George V has been the heir to the British Throne and thus, mistakenly being thought as the son of Queen Elizabeth II (instead of her cousin), we often forgot that like her Renaissance namesake, Queen Elizabeth the Second never married.
That fact alone might be able to explain why the Parliament did not really think too much about The Queen being a politically active monarch, but it sure made me think an alternate scenario where King George VI survives the War and either her father push the then Princess Elizabeth to marry, or maybe without her parents and sister being dead and she was practically left alone, she won't end up growing into a strong-willed, brilliant, but also bitter and vengeful Queen who spurred all the potential matches offered to her.
The name "Elizabeth" itself might also ironically being a much more popular choice to the greater populace, as with two Queen Elizabeths that never ended up married, the name ended up carrying some connotations not only for strong, independent women who fears nothing but also being spinsters who reject all men trying to woo them. The name "Elizabeth" did ended up being very popular with feminists for the very same reasons though.