I can't think of a way to actually use any kind of tracking cookies, even non-ad/sales/data-harvesting related that wouldn't be annoying in EU.
Of course, if you manage your own load balancing, could definitely combine a load-balancer pinning cookie (uuid) for "all" uses as a single "essential" cookie.
See GitHub.
You can't use the data for other purposes though.
Tracking without cookies requires consent no matter how you implement it. Claiming it to be essential won't fly if, say your Marketing or sales team has access.
Once it's used for other (technically non-essential) needs as well, one needs to find another basis for processing or ask permission for that second purpose(consent basis).
Also, if the LB cookie can be non-identifying, while fullfilling the stated technical purpose, it must not allow identifying users. So for LB cookies, one must not use a unique ID per user, but an LB ID instead. Something like "node1", "node2" etc...