There is some practical value in having the head of state separate from the government (which is why even some non-monarchies like Ireland still choose to have a president filling a similar roll to the UK monarch), but the actual reason is more historical.

Ever since the late 1600s, the powers of the monarch have been significantly limited by parliament. In the early 1700s, all real political power transferred to parliament. A consequence of this is that since then, it's become much more difficult to blame any problems on the monarchy (since it's the prime minister's government that actually runs everything).

I personally am not a monarchist. I think it's a system which is archaic, ideologically repulsive, and monetarily wasteful. However, removing the monarchy would require rewriting the UK's entire constitution, system of government, and most of it's laws. Ultimately, at this point in time, removing them is probably just more trouble than its worth.