Installing sprinklers in the datacenter is probably a bad idea. But around it it may pay off, the fire may originate outside the datacenter. Inside the datacenter it’s be great to have some phisical separation so not all is lost in case of a fire and an extinguisher or whatnot can be used on the burning component without effecting the whole system. Also installing heat sensors and monitoring those may prevent a disaster. Installing partitions or building separated server rooms could also help.

Yes, from a fire safety standpoint, more partitions in the building are generally a good thing, especially when they consist of actual rated fire-resistant firewalls (physical firewalls not the "iptables" kind). It's amazing just how effective a firewall can be. I've been to structure fires before where you can basically say in the aftermath "everything on the 'fire' side of the firewall is rubble now, and everything on the other side is completely (or almost completely) intact". Of course you can still get some smoke and water damage, and even a good firewall can be breached if the fire burns long enough. But generally speaking, they help a lot.

And even a closed door in a residential building can slow things down enough to make the difference between life and death. This is why the fire service encourages people to sleep with their bedroom doors closed and to have a smoke detector near said bedroom door.

The downside to a heavily partitioned building, especially a very large building, is that it may become a maze that is hard to exit, and lots of doors between different areas slightly increase the risk that somebody will have a brain-fart and lock/chain doors that should never be locked, or otherwise do something that effectively traps people inside. Note to everybody: never chain/lock/barricade a door that must be used to exit a building in an emergency, in such a way that it can't be opened from the inside.

Keep a fire axe under the bed to create a new doorway as necessary :-)

Plus in a pinch, critical data can be recovered from wet hard drives and SSDs (say if it didn't make it to offsite backup yet). Melted hard drives and SSDs, no.