However, the CPT had wide ranging powers under the Act and had the power to legally knock buildings down, he said.
Mr Cooke said the building was a "symbol of the city'' which was trying to reestablish itself after the devastating earthquakes, adding that church and community were intrinsically linked.
Trustees must consider the wider community of post-disaster Christchurch, and not just their own ecclesiastical interests, when considering the future of its cathedral, he said.
Mr Cooke said the key issue for Justice Lester Chisholm to decide on was whether the CPT was correct that the cathedral's ultimate fate was at its own discretion.
The trust was designed for ecclesiastical purposes, Mr Cooke said, so when it received a $40 million insurance payout, for example, it believed the money should be used for church purposes only.
But Mr Cooke argued: "They just don't have that power.
"The land was originally gifted by the city council to the church for the construction of the cathedral.
"It was built after raising funds from the community and has received significant funding from the council ever since.
"The cathedral is a public institution. The trustees cannot be free to do what they like.''
CPT says the Act did not apply in this case because it was superseded by a Canterbury Earthquake Recovery Authority (Cera) section 38 unsafe building notice, which demanded urgent action.
Even without the notice from Cera, CPT lawyer Jared Ormsby today said: "They do, in fact, have the power to deconstruct.''
Opponents to demolition have provided several alternatives to demolishing the cathedral.
Bishop Victoria Matthews has said anything other than demolition is far too expensive but Mr Cooke produced documents showing two private donors wanting to donate $14m towards restoring the cathedral.
The money was not accepted because trustees "did not want to restore'' the cathedral, Mr Cooke said.
CPT say they simply do not have the funds available for a maximum retention option, or a replica rebuild, with estimated costs now soaring to $109m plus GST.
The issue has become one of the major talking points in the wake of the devastating Canterbury earthquake sequence, sparked by a magnitude 7.1 tremor on September 4, 2010.
The cathedral's spire snapped in half and the building suffered major structural damage in the February 22 quake, which killed 185 people.
The hearing is scheduled to conclude tomorrow.