I wouldn't exactly say there is no failover. Although not very convenient, you can set up two DCHP servers in your organization. It does not allow a very efficient use of IP addresses when you have two or more DCHP servers which can fill in for another in the event of failure, but it is easily done.
Lets say you use a class C network and have 100 machines on the network. You have up to 254 assignable addressses. You set up two dhcp servers, one with address scope 1-128 and the other 129-254. Obviously if you have more than 128 machines, you MAY (maybe) have a problem or may need more IP addresses. However, in this case, the two DHCP servers can cover for each other if the other one fails.
The only real problem beyond that is that the user's IP address may change if they reboot. So long as they keep their computer on and their lease does not come close to its expiration time, the IP address does not change. In the case of IP addresses changing, you can deal with dynamic changes to IP addresses by using WINS.
What problems would cause the screaming?