Why don't flights fly towards their landing approach path sooner?
In general, IFR flights through controlled airspace use airways (highways in the sky) to fly between waypoints. The particular flight you show looks like it arrived via the N774 airway to a waypoint MARLN:

(skyvector.com)
The traffic flow around busy airports like Kingsford Smith (YSSY) in Sydney is usually structured using Standard Instrument Departures (SIDs) and Standard Terminal Arrival Routes (STARs). Your example was probably on the MARLN5 RNAV STAR:

(from the Jeppesen chart for MARLN5 at YSSY)
From somewhere after the JAKLN waypoint, the air traffic controller (ATC) would have instructed the flight to turn right to intercept their final approach path (probably to runway 34R).
All of this structure (airways and procedures around busy airports) exists to allow for an efficient flow of traffic that can be easily managed by ATC. There are many things to consider when these paths are designed:

avoiding conflicts between aircraft (e.g. between departing and arriving aircraft or between flights from different airports in the area)
restricted airspace (e.g. airspace reserved for the military or avoiding flights near sensitive areas, like nuclear power plants)
noise abatement (especially near large cities you want to avoid overflying the city center at low altitudes)
terrain (not really relevant for Sydney)

Nonetheless, one can deviate from these fixed routes. ATC might clear an aircraft on a more direct route if traffic and restricted airspace allows this (very common right now due to the pandemic). Some countries have even removed all high altitude airways and replaced it with Free Route Airspace.
The problem with setting an aircraft on a direct route for final approach interception is that this would have to be done far away from the airport. The aircraft needs time to descend and slow down (usually more than 100 NM). At this point they are typically not handled by the approach controller for the airport they are landing at, but still by the Area Control Center (ACC). This would require significantly more coordination between various controllers and is probably not very efficient in busy airspace. During the current pandemic with significantly less traffic, you might see it though.