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> First, why does your home office need globally unique identifiers for its devices?

For the same reason that the original plans for the Internet ensured that every connected machine was a peer of every other: a network of peers easily allows for new and novel services on the network.

> Second, how does having the MAC address make routing simpler?

It doesn't.

> Third, wouldn't temporary (privacy) addresses undermine this entire EUI-64 setup's efficiency improvements?

That's not the point. The point of this setup is to provide a way for SLAAC to easily create a stable IPv6 address to make DNS forward and reverse mapping on the LAN easy to manage. There's also an alternative method for stable address creation that doesn't use the system's MAC address.

> Now you're back to randomized data in the low 64-bits, so the router and PC need to have some kind of negotiation to know the IP addresses just like before anyway.

You really need to read how SLAAC works [0]. In particular, pay attention to the Duplicate Address Detection section, and note how DHCPv4 uses a similar method for determining whether or not an IP in a pool is safe to hand out.

After you've read about SLAAC and DAD, read about Neighbor Discovery [1]. This stuff is more well thought out and less complicated than you seem to think that it is.

[0] https://en.wikipedia.org/wiki/IPv6_address#Stateless_address...

[1] https://en.wikipedia.org/wiki/Neighbor_Discovery_Protocol