Of course they exist.

That assumption creates some unpleasant conclusions. To make sure I understand you, please consider the following scenarios.

Suppose that our descendants acquire a deep understanding of human brain operation. They build a machine which can generate a brain-description to given parameters, as different from any existing human as normal humans are different from one another. Given a description, a living brain and body can be built and a person created.

Suppose we generate 10^10 different descriptions. Do we now have a moral duty to instantiate them all in real bodies, because once we have some information-theoretical descriptions of them, they are "existing persons"? Note that we haven't simulated them; we just computed the single-moment-in-time initial states of possible simulations.

Never reviving the suspended me simply equals killing me, with all the moral implications of an ordinary murder.

Then, does reviving you once equal killing the potential second copy of you we could also have revived?

Does the public has a moral obligation to refrain from killing people?

A better comparison would be: does the public have a moral obligation to support minimal living conditions for all already-existing people, and keep them from dying from hunger or disease? I think the answer is yet, but it is not absolute; it works so far because the burden happens to be economically easily bearable. It might also work for reviving people if very few people will ever be frozen, so that the total burden of reviving is small. If ever it came to a real economic tradeoff, reviving people wouldn't necessarily win.

There is stuff there in those frickin' brains you might find amusing, funny, interesting, useful or aesthetically pleasing.

Giving birth to children, the old-fashioned way, and so growing new people also creates interesting new brains. Why would reviving ancient people (who were not outstanding thinkers or personalities in their own time) be so rewarding?

The question about diversity referred to the moral situation. You think there's a moral obligation to revive people, and you justify doing that instead of duplicating people because the duplicates increase the diversity of society. Is there a factor for diversity in your purely moral calculation, or do you think that morally it doesn't matter what new person you create, and diversity is only a selfish reason to revive a more interesting person?