Due to the distance from possible locations to attack NZ there is a lot we can do to deter aggression against us as we are well outside the range of possible air support for any aggressor. An ACF with a good supply of both anti shipping and anti aircraft missiles would be a daunting prospect to any would be aggressor knowing that they would be without air support but having to go up against a competent ACF. The big thing that NZ has on it's side is the tyranny of distance and that combined with a ACF will supply a significant form of DETERRENCE.
In other words an aggressors commander would know that any attack either by sea or air would be attacked by missiles for a significant period of time while they headed for NZ without them being able to do anything about it. That would be a deterrent to any one.
Not really....
How many fighters can the RNZAF maintain? I saw 28 mentioned above - let's take that as a given. That's a strike of no more than 20. What aircraft are they? F-35? That gives you a chance - stealth + 2x JASM-esqe weapons. Anything else? Nope. You compromise stealth and weapons load. A F-15E like platform will carry the weapons, but I'll lay a bet the RNZDF can't afford 28.... Also note you need to by the -ER, and how many can you afford?
What's the threat likely to be? Lets be 'realistic' and assume a blockade of SLOC to the east. The west and north is defended by Australia, so you don't need to worry about that. But, this is Five-Eye's waters, so the Red Team is going to be the best it can be - with a focus on air defence (to stave off the CVBG's). That's Type 052Ds at a minimum - probably Type 055s (knocking out NZ is going to be a major, if not main, effort). It's also going to have some Type 054As with it - and there's probably 2 - 3 SAGs. That's 250 - 300 VLS tubes for each SAG - and you have 3x P-8, 20x fighters and 40x ASMs.... Unless you want to cough up $$ you don't have an over-the-horizon targeting capability either, so something crewed has to come close...
The maths don't add up. You may kill one ship, but you lose your fighter capability. You can't afford submarines. You can't afford ANZAC upgrades to CFAR and you can't afford to replace them, so you've no navy worth anything. You have 3x P-8's, and you'll probably loose one. So when the SAGs leave and the SSNs role in, you'll have no way to defend or kill them. You've probably killed your Army too - F-35s are expensive.
So, for giving up your fighting Navy and your fighting Army you've killed ~1.5% of the PLA-N's major surface combatants. Maybe. If a Type 003 or Type 004 rocks up (unlikely I grant) your ACF dies even quicker - because you can't afford AAR or AEW&C. And because of that, you can't go north to support Australian or US operations in the SCS or anywhere else in the Pacific. They barely have enough tankers and AEW&C for themselves!
When you run those maths it's easy to see you don't have a deterrence factor by adding some fighters. You can barely find submarines, you gut the NZDF and to what end? Even worse, without the Navy, Army, AAR and AEW&C you are reasonably useless to coalition efforts - so your ability to support US, British or Australian operations (and garner those 'brownie' points for future use)* is reduced or negated. So without that guaranteed big sibling your deterrence effect takes a hit.
BLUF: An ACF for NZ dies quickly and undermines it's realistic deterrence
* not a criticism; it's a traditional central plank of Australian strategy