I have been let down by my google foo and have been unsuccessful in finding the reference that I have been looking for that shows an apples for apples cost demonstrating that the Izumos were cheaper to procure than the Hyugas, which in turn were cheaper than the corresponding destroyer (I cannot recall if this was the Akizukis or the Atagos).
The Atagos are bloody big (10,000 ton) AEGIS destroyers with 96 Mk 41 cells, plus anti-ship missiles - the works. And yes, they're more expensive than
Izumo. Most of that expense is the systems & weapons. The
Akizuki class is significantly cheaper than
Izumo, despite being much more heavily armed. That's what the extra 20,000 tons, built to military standards, costs. The
Hyuuga class also cost significantly more than the
Akizuki class. About the same price as
Izumo, in fact (the extra weapons & sensor fit presumably making up for the smaller size).
So, you won't get three of 'em for the same price as three frigates. You can probably get two for the price of three Akizukis, which the JMSDF calls destroyers but which correspond to frigates (mainly ASW, longest range AAW weapon ESSM) in other navies. But then what?
Izumo, on its own, is like a giant OPV,
apart from its helicopters. It has lower-grade radar etc. than current Japanese ASW 'destroyers'/frigates (& so does
Hyuuga), & close-in self-defence weapons only. If you don't invest in the helicopters or other aircraft (whether manned or unmanned) & the personnel to operate them, they're a waste of metal, burning up a lot of fuel. And if you do fill 'em up, then the price rockets.
Your arithmetic doesn't add up. The ships cost more than those you propose them as alternatives to, they should cost more to operate, & without a lot of expensive additional equipment & people to operate it,
Izumo has very limited usefulness. The JMSDF knows this, of course, but it has the equipment & people to make her useful.
Operate army helicopters off 'em? Then what flies off the LHDs?
You're proposing a reduction in capability, replacing planned ships with more lightly armed ships the value of which lies in their ability to operate weapons & systems you'd need to buy, but without proposing to spend the money to buy the extra stuff or hire the people to operate it.
It's been said that when comparing the weapons fit of
Hyuuga with an ANZAC I omitted the helicopters. Correct - but as I keep bloody well saying, the helicopters it can carry aren't part of the fit-out or included in the price. They're an extra which the RAN doesn't have, has no plans to buy, & which would make a massive difference to the price & operating cost.