Construction time (and consequent disruption of other traffic) is very much less for Suspension
Monorail than for Light Rail, and trams...

Unlike these,  a Suspension Monorail (SM) does not require digging up an entire length of road to lay tracks & reposition underground services so that they can be maintained later (as for Sydney, above, 16 March 2019). Only the pylon footings have to be built on site, spaced about 35m apart. The pylons and the track can be constructed off-site and craned in at off-peak times (Shonan railway pictured below left).

Moreover, later revision of underground systems would not bring SM to a standstill! (pictured below right- recent sewer upgrade in Wuppertal). In Wellington, no tunnels will be required.

So, in short, the entire track required for Wellington (from Railway Station to airport) can be constructed in 2-3 years with minimal disruption to businesses and traffic; whereas the plan for trams (‘Light Rail’) will involve at least a decade (and that may only be for Stage 1). A map and details of a possible city to Eastern Suburbs route is here, which you can expand to view detail.