On the contrary, there was no need for the late Queen Elizabeth II to do anything about it because we have the UK Supreme Court which rules on constitutional issues brought before it.
From Politics Review Volume 29, Number 2, November 2019:
"The creation of the Supreme Court was designed to protect the separation of powers within the UK political system. Until the Constitutional Reform Act of 2005 and the creation of the Supreme Court in 2009, the Law Lords in the House of Lords was the highest court in the country. This was referred to as the fusion of powers."
And:
"Due to the uncodified and evolutionary nature of the British constitution, the separation of powers did not exist in the same way, with members of the judiciary (the Law Lords) sitting in the legislature. The change was triggered not due to accusations of corruption within the Lords, but due to a desire to modernise the judiciary and to bring Britain in line with most modern democracies."
In the final analysis, the separation of powers is protected and the system worked. The Supreme Court ruled the Prorogation Of Parliament as illegal.
The Queen knew what she was doing. To refuse any Prime Minister was to set herself in the middle of a power struggle between Parliament and the Prime Minister. Constitutional Law scholars believe this would have resulted in a bigger constitutional issue than Brexit has been.
The Queen wisely avoided that problem knowing the Supreme Court is there as the final arbiter on constitutional issues. In such a situation, the Monarch need not act or appear to subvert the Government.
If we didn't have a UK Supreme Court, you would no doubt have had a point and it would have created a massive constitutional crisis. Just as well we already had one!
As for the Irish President, they have the following limited powers:
the right to refuse a dissolution of the Dail where the Taoiseach "has ceased to retain the support of a majority in Dail Eireann";
the right to refer Bills to the Supreme Court to test their constitutionality;
the right to refer Bills containing matters of national importance if a majority of the Seanad and one-third of the Dail present a joint petition to this effect;
the right to address the Houses of the Oireachtas and the Nation (the text of any such address must have received the prior approval of the Government);
the right to assist in resolving a conflict between the Dail and the Seanad regarding what constitutes a Money Bill;
the President's assent is necessary to the abridgment of time for the consideration of a Bill by the Seanad.
However, the reality is that "most of these powers have never been invoked and only the right to refer Bills to the Supreme Court has been exercised with any frequency (12 times in all)."
In terms of the British Monarch, their powers as follows:
"....main functions as head of state are to appoint the Prime Minister, and all the other ministers; to open new sessions of parliament; and to give royal assent to bills passed by parliament, signifying that they have become law...
The King also chairs monthly meetings of the Privy Council, to approve Orders in Council; he receives incoming and outgoing ambassadors; he makes a host of other appointments, such as the senior judges, but in all this he acts on the advice of the government. He has a weekly audience with the Prime Minister, and receives daily boxes of state papers for his signature, and for information. He also has regular meetings with senior officials of all kinds. "
But the role we most often see the Monarch in is their role as Head Of The Nation. Main functions:
"....the Sovereign acts as a focus for national identity, unity and pride; gives a sense of stability and continuity; officially recognises success and excellence; and supports the ideal of voluntary service. This role has been fulfilled through speeches such as the Queen's address to the nation at the start of the Covid pandemic, and annual broadcast on Christmas day; through giving honours to recognise public and voluntary service; and through visits to the armed forces, schools, hospitals, charities and local organisations.
The Queen carried out just under 300 public engagements in 2019, and Prince Charles 520; but in total 15 members of the royal family carried out 3,567 such engagements. These include national occasions such as attending the Cenotaph for Remembrance Day, or the Trooping The Colour; but the majority are visits to all parts of the UK, to recognise and support the work of local public services and voluntary organisations. The King and other members of the royal family are patrons of over 1000 charities and organisations in the UK and the Commonwealth."
www.ucl.ac.uk/constitution-unit/explainers/what-role-monarchy
The Royal website states "The Sovereign no longer has a political or executive role, he or she continues to play an important part in the life of the nation."
And this in addition to the above can be seen in the UK's rankings in the Global Soft Power list where we're second only to the USA. The Republic of Ireland, on the other hand, is still just about in the top 30.
Overall, the Irish President and the British Monarch are very much ceremonial roles. You most often see them in their respective roles as Head Of The Nation. They're not all that dissimilar in practice and both have some political involvement in different ways.
But it is not their main roles - their ceremonial Head Of The Nation role is. So, this is not really an argument for the abolition of the Monarchy. If we want the King to have the power to personally refer Bills to the Supreme Court, we could do that. But we've no real need to. The system itself works as the Supreme Court proved.
The King reigns, but does not rule. The same could be said of the Irish President.