Steel is cheap and air is free. The actual expensive costs in any frigate build are the sensors and weapons systems installed therein, hence IMHO transferring the systems from a frigate build to a flat deck will not make the end result inherently cheaper. A frigate is designed for high intensity modern combat whereas the LPD isn't and the LPD wouldn't meet all of the NZG policy requirements.
I agree with the steel is cheap and air is free comment as I have used it myself. My concern is that in the event of a shooting action anything NZ has will be extremely vulnerable given the lack of long range weaponry of NZ vessels. As noted in your own posts the threat from modern ordinance will overwhelm even the best equipped. So let's be realistic in our thinking regarding the use of mini flat tops in the context of NZ. In the event of a coalition operation one of the two GP frigates would be available to participate unless the LPD was desired. For SP operations the force projection of an upgunned LPD with its 5" gun and helicopters plus an embarked force with high speed CB90's would be an overwhelming force of diplomacy.
All I am suggesting is that versatility is the key. A quick search today revealed many articles from writers around the world extolling the benefits of these ships as MrC has alluded too repeatedly. Like the Absalon class that I still think is a good GP frigate the Algerian LPD offers more. Some of what I read today stated that the high crew numbers was due to reduced automation. In the best interests of efficiency a design change to incorporate labour reduction systems would be a good investment in the long term. Another change I would consider would be another hull stretch, if possible, from the current 143m, to 160m. This would be primarily to increase bunkerage of fuel to extend the range. The added room would also allow room for an additional helo.
What stands in the way of this type of a change in organization is the want to be something that you can never be. New Zealand will never be afforded the high end AAW capabilities of a Hobart or the offensive capabilities of TLAM.
If a frigate sensor package along with a comparable weapons load including 533 mm heavy torpedoes as planned for Damen crossovers this would be a significant capability for a navy the size of NZ. The country has always punched above its weight from a people perspective. The time is right for RNZN brass and the elected ones to sit and openly discuss realistic options.
Like anything that is multipurpose it's never going to be as good as a uni tasker. Canada was guilty of having a unitasker fleet at the end of the Cold War. Even today the concern for what replace our frigates and destroyers will hamstring the government if it fails to head what so many are saying about flexibility.
As much as I would like to see NZ with ships similar to Australia to take advantage of economies of scale during production I feel NZ will not need what OZ will be selecting.
Like others I feel RoK built vessels will offer the cost advantage and it's up to smarter people than I to ensure the Navy and the Government get what is needed.