The problem is that the daemon dhcpd is still managed by old style SysV init scripts, but must be emulated by systemd with its service isc-dhcp-server.service. This makes it more error prone and mixed up management of both init systems. Usually you find (error)messages in the systemd journal with journalctl, with SysV you have to look at /var/log/syslog. Now you will find some uncompleted messages in the journal and some more detailed messages in /var/log/syslog. This was confusing me.
So look at /var/log/syslog if you find more detailed information why the service isn't started by systemd on boot up. I used
rpi ~$ grep dhcpd /var/log/syslog