I agree with what you are saying about the government changing with elections, but I think that is similar for monarchy. It is not done through elections, but I see the people as individuals rather than a single entity that carry the blame of all those that came before.
The monarchy really isn't the same as it has no power (although, it has also had no power at points in the past also). Though the title is still there, it isn't the real role of a monarch, who would pretty much have dictatorial power over a nation. It is a head of state position.
In the end, I just do not understand the point of spending millions on something people aren't going to agree on, anyway. Head of state will just be another point of contention that people won't be happy about, either. And we could always end up having Boris Johnson as head of state and Liz Truss as PM.
The vast majority of the tax is spent on the royal properties, of which I believe there are about 900. This would still need to be paid, unless the nation decides to sell them off privately, which would be a shame as access to the public could be lost.