I doubt negative gearing affects the rental rate much. Possibly in the single digit percent kind of area, but nothing like what 'a fraction' implies. Statistically, rental rates have an extremely strong correlation to vacancy rates. Although there are claims that when negative gearing was briefly abolished, rents went up, they actually went down in many markets and up in a few, but all of them were just following vacancy rates like they always have. Part of this may have been that it wasn't abolished for long enough to see the effect of the reduction in new stock encouraged by negative gearing, but it's pretty terrible at doing that (90% of NG investment is in existing property) so that probably wouldn't have been much.

The yields are low because rents have to be affordable to most of the population, whereas banks will lend ridiculous amounts of money to speculators for houses, fuelling the bubble.

All in all, NG (in concert with the capital gains tax discount) mostly encourages speculation, artificially increasing house prices, so it should be at least restricted to new-builds only.