In my time, automated systems really only consisted of engine room CO2 or Halon deluge (both of which would kill any people remaining in the space), similar systems in the turbine enclosure (which was sealed), and fitted eductors (electrical and firemain powered) for water removal. Everything else required people power.
A repair base (an ANZAC ran two) consisted of about 15 people. An IC, board marker, comms, (3 people), fire team (3 people IC attack hose, waterwall), leak team (3 people), rovers (1-2 people), first aid (1-2 people), spare (2-4 people). If we had a fire, those spares became boundary coolers and hose managers (fully charged hoses are heavy and required at least one person per hose to move for the fire team). In an incident those 15 people are really really busy, and would need supplementation within about 30 minutes from exhaustion.
We would often move people between repair bases depending on the situation, or draw from a central (any non allocated people typically mustered in the galley, perhaps another 10 people at most) location. We would have another 10 odd people in the engine spaces and about 4 on electrical, tasked with getting machiney back online.
So all up damage control used about 50 people from a 180 person crew. In bad situations we would pull people out of the bridge, CIC or the like. Everybody on the ship had damage control training and could do a broad range of advanced fire, leak stop or first aid duties.
Everybody completed an offsite course where you were firstly drowned (nearly) in a flooding simulation, and then burnt (at least it felt like it) in a fire scenario. I also remember being deliberately gassed with tear gas and having to fit my mask in a room full of it (it stings). This training was better by an order of magnitude than anything offered in civilian industries.
For full OLOC (deployment to an operational area) we would train for a multi fire/flood scenario, lasting in the order of 4-5 hours. They would let us sleep for about 2 hours and then make us do it all again. And we would do this for about two weeks for the assessment, with about 2-3 months beforehand to prepare. We would exercise in total darkness, and several exercises would be deliberately done such that you would fail.
Nearly everybody on the ship (all 180 odd on an ANZAC) would get time in a repair base. I've been in a fire team with my XO. I have found nothing in civilian life that compares to the intensity of an OLOC workup. Few things are as exhausting and push you to your limits.
When you read about ships that have taken significant damage and survived, its because of the above. Numbers of people, advanced training, stress capacity and fatigue management.
Nowadays, engine spaces are fitted with water based hifog systems, which are much safer and just as effective as CO2, meaning they can be used as a first line rather than last line defence. Sealed enclosures for engines is more widespread, rather than open engine spaces, which is much easier to contain and extinguish a fire. These reduce the load on a fire team.
I think ships like the Mogami make much greater use of CCTV, full ship water sprinkler systems (like you would find in an office building) for automated fire suppression. I would suggest these systems are fine for peacetime where a fire may be because a bin caught alight, or say an engine leaked and ignited.
In say a missile strike however, you would likely loose power, the cameras would be damaged, the firemain supplying the sprinklers would be ruptured, and 30% of the crew would be incompacitated.
The ability to recover here would relate to redundancy and robustness. Can you reroute power and firemain to get the automatic/remote systems back online. Were your bulkheads and doors strong enough to contain the impact to a limited ship section. Did you have enough valves to isolate a damaged pipe without loosing the whole system. Did equipment stay on its mounts following an impact. Can you ballast. Can you do all that at once. How much stability margin does the ship have. For a low personnel ship, these systems/features become very important.