I think the focus on negative gearing is a bit of a distraction. As many have pointed out, properties are only negatively geared because they are losing money, which makes them looks like poor investments in the first place.
What people miss is on a whole, property actually makes money through capital gains on sale of the property, which will easily offset any of the operating cost that's been accrued. Note though double dipping doesn't happen because what has been deducted on negative gearing is taken away from the initial value of the property, thereby attracting more capital gain tax at the end.
The primary problem is, land value and hence property value naturally rises over time and is unavoidable. As cities grow, they spread out or they get more dense. Therefore an single property will be demanded by more people as it closer than more properties (as cities spread, or more city centres crop up nearby), and lower density than nearby buildings (as density of the area grows). No amount of anger will change the fact that land is a scarce resource, particularly convenient land. And so that price signal is important to allow that land to be used as efficiently as possible (you couldn't want a giant farm near a CBD when it could house and cut commute costs for 50k people).
What we really should be doing is discouraging profiting off this natural and unproductive growth in value. Perhaps this could take the form of having a different capitals gain tax tier explicitly for residential properties. The other aspect is changing the primary residence exemption to be that you have to have lived in the property for at least 50% of the time you've owned it for, rather than just the last 12 months. Though overall, this would need to be designed carefully to prevent disadvantaging people who are simply wanting to upsize, or simply to relocate to an equivalent location.