Thank you for a great question. You are right in your understanding!
1- If you have statically assigned devices on your LAN, these devices will not be affected by the failure of your DHCP server.
2- If you have reservation assigned devices on your LAN and the DHCP Server fails then these devices do not necessarily stop communication with the LAN, however there are a couple of things to keep in mind:
How long the IP address leases are set for.
These leases are typically 8 days (but this is up to the server administrator)
How much time is remaining on the reservation assigned leases.
At the time of the DHCP server failure if a mission critical device has say 7 days left on the IP address lease and the DHCP server is restored in less than the remaining IP address lease duration then mission critical services will not be affected by the server failure. However if it takes longer than the lease duration to bring the DHCP server online then your mission critical devices and the services they provide will most definitely be affected.
When it comes to which is better well.....it depends (I hate answers like that...lol). Remember that DHCP is a Dynamic Host Configuration Protocol which means we can configure a lot more than just handing out an IP address such as default gateway, primary and secondary DNS server, domain names... and more. So in that context statically configuring say 25 servers would not be bad to reconfigure but if you have to statically configure 1000 servers then you are in for quite a task. So DHCP can help us with the management of these other configurations and avoid mistakes. Imagine a scenario in which you need to reconfigure the network's subnet mask, again 25 servers is not so bad to statically manage but 1000-2000 servers statically managed can be a bit complex and decentralized....insert a DHCP server, a simple reconfiguration of the DHCP options, it can hand out the new configuration to all those servers and all through centralized management.
Now this leads us back to your question still "What about a DHCP server failure," in a large environment they will plan for DHCP failure through DHCP clustering in which the DHCP servers can communicate with each other and become aware of a failure then respond accordingly.
Let's sum it up:
Smaller environments can benefit from static assignment in case of a DHCP server failure if money/scalability is an issue.
Larger environments can most certainly benefit from static IP assignment in case of a DHCP server failure, however the greater the amount of statically assigned devices the greater the complexity in managing configurations as well as reconfigurations. These networks can benefit from implementing DHCP server failover and pushing out configurations through DHCP.
So in the end both network types can benefit from static assignment each with their own considerations.
So I hope this helps, as there is not a one-size-fits-all answer!!