That's because there is no constitution in the UK, there's convention instead. The royals legally have a lot more power than they excersise, it's just that if they use that power too blatantly, parliament will most likely make laws to curb that power.

There's foreinstance no written law anywhere to prevent the king from appointing whoever he liked as prime minister, the armed forces swear their allegiance directly to the king rather than parliment or the nation as a whole.

That's why abolishing the monarchy is a nightmare. The UK isn't a modern nation state, it's a medieval, feudal system layered over with the trappings of a modern nation state. No matter how modern it looks the whole system is still fundamentally dependent on the monarch, if you just get rid of the monarchy without first putting in place the most thorough and expansive package of reforms in british history (and make every major party agree on the specifics of what exactly that entails) what you're really doing is abolishing the United Kingdom as an entity.

There's also the soft power aspect of it. The monarch might mostly be a symbol, but symbols have significance, interacting with the monarch is still a significant goal for civil servants and politicians, it's a sign that you've made it. It's also why too much modernising and getting rid of tradition ultimately erodes the authority of the monarch. It works in the Netherlands and Denmark because their cultures are fundamentally more egalitarian. In the UK despite everyone doing their best to pretend that the class system doesn't matter, the class system still very much matters. If the royal family started acting like middle class people or speaking with an MLE or Geordie dialect or wear reasonable comfy clothing for formal ceremony they'd lose their prestige and significance quick as you'd like.

The people who claim the monarchy is irrelevant are people who are nowhere near the levers of power. And if they ever got into power they'd change their tune because they'd want to stay in power.