Sure, but for me ironically it is down to the Symbolism. For the most part, people tend to judge a country more on the first thing they see, a lot of people see the monarch as an introduction to British Values and so on, but this like i outlined isn't much of an accurate representation of Britain, its more like a representation of Britain during the 1850s, we're in 2018 just now and it makes no sense to keep a inaccurate representation such as the Monarchy. Second of all, making a country that is a Republic makes more sense even in the realm of Representative governments. Many Republics have their Prime Minister who is a representative of the electorate and the government, then they have a president who is someone of a separate party that is there to mediate confrontations between the two, and is there to add an extra level of control to the people. Since having the Leader of the Opposition is great and all, but when you have a situation like just now where you have a Conservative Majority government with Theresa May in charge (who no one voted for, she just showed up) you could have a president who is a member of the Labour Party. Which would send either two messages, either the General election was a marketing failure that lead to a Conservative lead that when the Presidential elections came up everyone changed their mind, or that the Conservatives represent British Economic values and the President represents their Social values, it still wouldn't make a Democracy, but for the most part it would make more sense than having a very old tradition in charge that barely does anything other than collect dust and our tax money.