the dangerous missile attack modes are the alpha-strike ones, and shields are strongly contraindicated. the quantity of hit points you surrender when you replace armor with shields is immense. looking at Mercury, even granting size 20 shield generators instead of the existing size 10, right off the top you'd be losing _half_ the total durability. some fraction of armor never gets used tis true, but with 12 levels of armor the fraction that outlives the ship is going to be pretty small.
even looking at AMM spam, a conspicuously shield-friendly use case, if just 25 missiles per increment are incident upon shields, the hypothetical all-shield variant would succumb before the incumbent design be likely to take any internal damage. the number of volleys involved is also significantly less than those accursed all-magazine ground bases will spit out.
That is only in some very niche situations where the shields are not better. In most scenarios there will be more than one strike such as fighters, FAC or missile boats of all kinds. They will reload and come back.
The idea with the shields is that you can survive multiple larger strikes not just one strike. In my opinion if you are that close to collapsing you will not survive a second strike anyway so it does not matter if you barely survive the first. You have to assume that you are able to blunt the strike enough so you take some of the force on the shields, this saves allot of resources in so many situations as you don't need to destroy every missile coming in... armour don't regenerate.
In the cases that the shields and whatever armour you have don't hold, most of those cases you are likely not going to survive the battle anyway. In terms of AMM you either deal with it some other way or you retreat so you can regenerate the shields.
In general I find that surviving multiple strikes are way more important than surviving any individual strike seen to the whole. The other thing is missile yields... when missiles get to nine or more in yields shields actually start to become quite valuable even from a pure damage perspective. A ship will be destroyed long before it's armour are gone and certainly damaged even earlier.
It is probably worth being explicit about the type of combat under discussion. I get the sense that some are talking principally of vs. NPR combat while others are speaking to Player vs. Player combat. These are two very different cases and it will be helpful to specify which is being discussed.
For example NPRs (e.g.
Precursors) do not tend to launch multiple large strikes as from box launcher fighters or reduced-size launcher missile cruisers, rather they tend to launch continuous strikes with full-size launchers until their magazines are exhausted. In this latter case the recharge time of shields is significantly less impactful as shields do not recharge appreciably in the typical 10-20 seconds between missile waves. Similarly, AMM spam is a tactic somewhat unique to, certainly a signature of, NPRs, and for players who principally play against NPRs it is certainly not a "niche situation" which can be easily dismissed as it will come up against nearly any NPR which uses missiles in some capacity. While it is true that these tactics are not particularly clever or indeed difficult to beat on even footing, often in combat vs. NPRs the game is more about finding ways to beat an NPR which is ahead in tech, whether a spoiler race or an NPR that rolled high on the starting conditions, without having to wait around camping a JP until the tech gap is closed.
On the other hand in Player vs. Player games the situation is very different as player races will use more diverse tactics and will tend to avoid the most straightforward or spammy approaches that NPRs are reliant on, thus a wider variety of use cases arise many of which are not seen against NPRs. Notably player tactics tend to be based on using speed and alpha strikes rather than continuous fire, under such circumstances shields for example are far more efficient. Similarly, player races will tend to be very even in tech (by design, otherwise the game wouldn't be that much fun) so the problems of e.g. AMM spam are not nearly as drastic as they are against NPRs with a tech lead even if a player does choose to use such a tactic.