Do you have a source for your comment "DHCP doesn't check..." ? Because the ISC DHCP server ( the default one EdgeOS uses) does check:
https://linux.die.net/man/5/dhcpd.conf
Ip Address Conflict Prevention
The DHCP server checks IP addresses to see if they are in use before allocating them to clients. It does this by sending an ICMP Echo request message to the IP address being allocated. If no ICMP Echo reply is received within a second, the address is assumed to be free. This is only done for leases that have been specified in range statements, and only when the lease is thought by the DHCP server to be free - i.e., the DHCP server or its failover peer has not listed the lease as in use.
If a response is received to an ICMP Echo request, the DHCP server assumes that there is a configuration error - the IP address is in use by some host on the network that is not a DHCP client. It marks the address as abandoned, and will not assign it to clients.
If a DHCP client tries to get an IP address, but none are available, but there are abandoned IP addresses, then the DHCP server will attempt to reclaim an abandoned IP address. It marks one IP address as free, and then does the same ICMP Echo request check described previously. If there is no answer to the ICMP Echo request, the address is assigned to the client.
The DHCP server does not cycle through abandoned IP addresses if the first IP address it tries to reclaim is free. Rather, when the next DHCPDISCOVER comes in from the client, it will attempt a new allocation using the same method described here, and will typically try a new IP address.
Same story for the DNSMASQ DHCP server
http://www.thekelleys.org.uk/dnsmasq/docs/dnsmasq-man.html
By default, the DHCP server will attempt to ensure that an address is not in use before allocating it to a host. It does this by sending an ICMP echo request (aka "ping") to the address in question. If it gets a reply, then the address must already be in use, and another is tried. This flag disables this check. Use with caution.