OK - so in some ways this post is a little late, and runs the danger of no longer being topical. But sometimes I prefer to sit back and think about the issue for a bit longer before just shooting from the hip.
First with regards to the penalty - my belief is that it did not go far enough. Given that the covenant existed when the property was bought, the line should have been taken that this was a condition of the contract that the property was bought with. By cutting down the tree he has breached the contract and forfeited any right to the property. Sod the fine, take away the dirt completely and that would make pretty sure it would not happen again.
Should the covenant actually have existed - no. Effectively under the current regulations the Auckland City Council confiscates part of your land for the "crime" of allowing a tree to grow taller than 8 meters. This is fundamentally unjust, and in future is probably going to mean that people:
1) plant less natives
2) never allow a tree to grow tall enough to reach protected status.
What should really happen? I believe that our large and historic trees are worthy of protection and are not exactly a replaceable commodity, so the need to apply for resource consent before destroying a large tree can stay. But the response to the consent either needs to be a yes (go ahead) or an offer to buy the tree (and whatever land is required to support it - with the required easement). IE the consent process is just used to give the opportunity for an offer to be made - not a perfect capitalist system, but a compromise I would be happy with. And I'm pretty sure most people would gladly sell their tree for EG $10,000? This can be funded either through specific fund raising for that tree - or more likely funded from the parks / nature budget.
In Brisbane there is a seperate charge as part of the rates that is dedicated to buying back land and putting in greenbelts. Personally I think this is a great idea - and the concept can easily be spread to buying back specific trees.