Because, by having a (non-political) Monarch we can respect, we are freed to be properly disrespectful towards politicians, while remaining loyal to our country. Without a monarch, loyalty can demand political submission.
Also, the British monarch is like the king on a chessboard. He cannot attack. But by occupying his square he prevents others from doing so – politicians who long for the supremacy that monarchs have, who yearn to be escorted by booted cavalry and greeted with trumpets, and who want us to respect them even when they don’t deserve it. Especially when they don’t deserve it.
It’s not an accident that most of the longest-lasting free, law-governed countries in the world are constitutional monarchies. Yet we seem keen to throw this advantage away, because we no longer know who we are or how we came to be so free and happy.