This code is usually there for a reason and a unikernel will have to implement large swaths of this code anyway.
Networking isn't trivial and I don't think anyone will be reimplementing the TCP/IP, UDP/IP, ARP, DHCP and more stacks without breaking in a few bugs themselves.
Example, modern TCP congestion control requires a very precise packet pacing and timing.
Another example, TCP retransmission will be required at some point, the code doing this will have to run side-by-side with the app. This will also be some amount of code.
And all this just piles up and up.
The only real advantage I see for unikernels is that because all the hard work is done by the hypervisor they don't have to bother implementing device drivers and task scheduling but end up either replicating or using the hypervisor's own networking stack and a bunch of other subsystems.