Won't help
When I lived in NZ, in the late 1990s even with Southern Cross you could get a T1 from Los Angeles to Auckland for about $9k/month.
The problem was that getting it delivered beyond Auckland cost $30-45k/month
There was (and is) a pretty cosy duopoly in New Zealand and the newcomer made it pretty clear that all they were allowed to do was undercut Telecom NZ by a little - introducing anything resembling actual competitive pricing would put their PSTN interconnects at risk.
2 years prior to Southern Cross going live, Telecom NZ bought up - and then sat on - all the surplus satellite bandwidth into the country. Doing so was cheaper than allowing competitors to buy it and then force prices down.
Telecom NZ is only slowly being brought to account for the illegal/anticompetitive practices they engaged in during the 1990-2004 period and the fines really only amount to a slap on the wrist with a wet bus ticket as they succeeded in putting anything they regarded as a business threat out of action long ago.
It's amazing what you can get away with when you effectively own the government (including making investigations into illegal behaviour simply "go away" by ministerial order).
REANNZ might get cheaper connectivity but they're going to find it very hard to sell to 3rd parties unless there's a lot tighter control over the last mile than there currently is, even with the recent changes to break up the lineside monopoly.