Compulsorily aquiring land for base housing would not meet the requirements, so would definitely be contested in the courts. Moving the base away from the main population centre probably makes it dificult to recruit the sort of technical skills they need.And into economics and ownership rights.
Outside of the US, 'eminent domain' is usually known as expropriation or compulsory acquisition. In New Zealand, compulsorily acquiring private land falls under the Resource Management Act (RMA). And it follows a bureaucratic process.
Kiwi landowners faced with compulsory acquisition [1] have the right to full market value of their land as well as disturbance payments and/or compensation for any resulting business losses, increased mortgage payments on replacement properties, etc.
Base housing isn't directly related to the Mogami class but it does beg the questions of whether bases market housing should have been allowed around bases and whether existing bases in built-up areas should be retained. Compared to funding new bases, procuring a few Mogami class will look like a bargain ...
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[1] AFAIK, compulsory acquisition under the RMA assumes the actual use of acquired properties ... not just holding on to lands that might be handy in future. Indeed, if the land is not repurposed immediately, resident owners have the right to stay on the property until its use is reallocated. Point being, it is a potentially messy process that dictates careful planning and scrupulous execution.
Anyway, back to topic...
