What a government does or doesn't do to or for the people can have moral content, but its inner workings do not. An absolute monarchy that treats citizens well is more moral than an oppressive elected government. Lacking any moral content, then, the powers of each part of a government should be strictly by the letter of the law. She should have the power until it is legally stripped from her.
The Queen is an authority figure and the symbol of country, but the powers that she does possess are overshadowed by the powers and actions of Parliament. On paper, she has designations and jobs, but in practice, Parliament does whatever regardless of her. It would be more balanced if she had more power over them. She's an authority figure that currently lacks authority.
Monarchies are obsolete holdovers of different eras, even where the role of the monarch is primarily ceremonial. As the veto itself shows, even ceremonial monarchs retain power. The idea that an unelected, hereditary, monarch holds any power in a democracy is adverse to the ideals of democracy and should be abolished.
The monarch of the United Kingdom is, as are most contemporary monarchies, a historical artefact, with little (if any) political power, their role is largely ceremonial. Refusal of royal assent is rarely exercised any more, and the main reason is, as you suspected, respect for democracy. Conversely, the last time royal assent was refused in the UK was in 1708, when Queen Anne vetoed the Scottish Militia Bill.
Elected officials, on the other hand, are not going against democratic structures if they exercise their veto powers.