doesn't that depend on the specifics of how you replace it? I mean to start with it's likely to bring about the downfall of the whole aristocracy including the house of Lords.
There are several reasons I want rid of the royals, one of the keys is that they have over the centuries prevented a proper written constitution, and set of rights for british people. Only ceding some rights to aristocracts, who in turn got bullied by the people to handing a bit out to the general populous such as voting rights.
Those aristocrats, including the royals, still hold the vast majority of power and influence and wealth in this country. They own most of the land, most of the wealth, much of the city property, most of the coastal waters, and of course most of the powers of lawmaking.
The monarch gets to have first dibs at amending any bills, then it goes to the house of commons, but, of course, on the tory side there are many non-commoners, many aristocrats in the government, so some of them get to dabble here, then it goes to the Lords where thanks to hereditary peers, and tory life time peers the aristocrats get a final block on our laws.
Get the aristocrats out of our system, they've proven over the centuries to be self servicing. Let the people rule.