IPv6 would help both enormously.
In the long term, yes. In the short term, going offline for the 93.69% of their users who don't have IPv6 yet would certainly be seen my most as a completely dickish move - I'm pretty sure their investors would be upset, for one thing.
Lower latency on routing means faster responses.
How does IPv6 yield lower latency? If anything, the latency on IPv6 is often slightly higher than IPv4 owing to the prevalence of IPv6-over-IPv4 tunnels where native IPv6 interlinks aren't available, along with larger headers slightly increasing the latency of cut-through routing.
IP Mobility means users can move between ISPs without posts breaking, losing responses to queries, losing hangout or other chat service connections, or having to continually re-authenticate.
Does anyone actually implement IP mobility? It requires support from your ISP, and I've not heard anything about any ISPs implementing it.
Autoconfiguration means both can add servers just by switching the new machines on.
DHCP does pretty much the same under IPv4 - I can't see this being a boon to Google/Facebook. (TBH I wouldn't be surprised if their infrastructure was too complex for any of these protocols - they've probably got some home baked protocol for doing that stuff).
Because IPv4 has no native security, it's vulnerable to a much wider range of attacks and there's nothing the vendors can do about them.
So no different from IPv6 then... both protocols have ipsec support (I think it's mandatory for IPv6 whereas the IPv4 version is an optional backport, but all major OSes support it in both cases so that's neither here nor there). However, ipsec use is currently pretty much reserved for VPNs - you can do adhoc ipsec but no one does. About the only thing you get from IPv6 is that IP addresses are much sparser, so scanning/attacking by picking addresses at random isn't effective.