The short answer is: "It's complicated".
I'll try to keep it as simple as possible, but first we need some background.
The announcement of Philip's engagement to Princess Elizabeth was made on 10 July 1947. Ahead of this, Prince Philip had become a naturalised British Subject on 28 Feb 1947 and adopted the surname Mountbatten from his mother's family. At this time he also renounced his Greek citizenship, and his right of succession to the Crowns of Denmark and Greece.
This was all to do with worries of public reaction to a perceived "foreign" prince marrying the heir to the British throne in the immediate aftermath of the Second World War. It was much better to stress the fact that his great-great-grandmother was Queen Victoria, that he had served with distinction in the Royal Navy during the war, and that he had formally renounced his claim to the (foreign) thrones of Greece and Denmark.
[Interestingly, In 1957, by a court ruling in the case Attorney-General v. Prince Ernest Augustus of Hanover established that all descendants of Sophia of Hanover - including Philip - were already naturalised British subjects under the terms of the Sophia Naturalisation Act 1705.]
But the whole concept of "Britishness" is fraught with difficulties. Great Britain is the union of the countries of Scotland, England and Wales. The name was defined in the first sections of the Union with Scotland Act 1706 and the Union with England Act 1707. The United Kingdom is the union of Great Britain and Northern Ireland. Again, the name was defined in an Act of Parliament, this time the Union with Ireland Act 1800. The name was originally the United Kingdom of Great Britain and Ireland, but this was later amended to United Kingdom of Great Britain and Northern Ireland when southern Ireland became independent of the UK (see below).
I did say it was complicated! I have seen that diagram fairly described as:
"one of the most complex Venn Diagrams an everyday schmoe will ever be
expected to Grok."
Scotland and Northern Ireland have always had different legal systems from that in England and Wales (even after the Acts of Union), and since further powers have been devolved from Westminster, the situation has become even more complex!
One thing that has emphasised the "British", rather than "English", nature of the monarchy is the range of titles held by each member of the Royal family.
As you say, Prince Philip (then, just Lieutenant Sir Philip Mountbatten, K.G., R.N.) was granted the Titles "Royal Highness", "Baron Greenwich", "Earl of Merioneth" and "Duke of Edinburgh" by Letters Patent from the King just before he married. The grants were gazetted on 21 November 1947.
This gave him titles in all of the nations of Great Britain. Obviously, this would not only have reinforced Philip's British credentials, but also emphasised the "British" nature of the Royal family itself.
So why wasn't Philip also granted a title in Northern Ireland?
The relationship between Great Britain and Ireland has always been complicated. Let's limit ourselves here to the first half of the twentieth century.
From 1922, the southern part of the island of Ireland became independent of the United Kingdom. Northern Ireland exercised its option to remain within the UK, although a significant minority in Northern Ireland wanted to be reunited with the independent south.
At that point, the Irish Free State in the south remained a dominion of the British Empire, which meant that its people remained British subjects. This remained the case until the Ireland Act of 1949, even though - in Irish law - Ireland had been virtually a republic since the end of the Second World War, and perhaps even earlier.
Now, the marriage of Prince Philip to Princess Elizabeth was less than 18 months before the Ireland Act of 1949 came into effect. Granting Philip titles in Ireland at that time would have been insensitive at best. This presumably explains that particular omission.
In recent years, the situation has improved considerably, which is why it was possible to grant William the title of Baron Carrickfergus in 2011.
In fact, on 22 February 1957, the Queen granted Prince Philip the title of "Prince of the United Kingdom of Great Britain and Northern Ireland". This was gazetted on 22 February 1957.
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