Sydney is a slightly different beast though. Its transport problems stem from a mixture of geography, history and lack of/inept planning.
Its roads are generally thinner and crazier due to being a more "organic" in its early planning compared to melbourne (which is built in a planned grid). Sydney literally tore up and destroyed one of the biggest tram networks in the world and converted the roads to automobile.
Meanwhile the combination of the harbour, sea to the east, blue mountains to the west create an increasingly geographically constrained city. Transport options are severely limited out to the eastern suburbs (cynically, partly by desire, they are also the wealthiest suburbs in general). Contrasted with melbourne, which is built on a massive flat plain around a bay, Sydney terrain encompasses hills and valleys to a far greater extent further limiting the engineering options.
Finally, sydney's main airport is comparatively close to the main CBD (almost half as close as melbourne's) which is further limiting the available land within the central area, and resulting in requirements to build a second airport out west to try to increase air capacity to the city.
The result, along with australia's cultural and historical proclivities is a city almost in constant congestion, highest house prices, and with easily the longest commutes in the country. (keeping in mind when viewing comparable stats, that although sydney is out in front, I felt many sydney-siders will rationally try to compensate/substitute their travel times to avoid the congestion).
Lived in both myself. All major cities have congestion, but its at another level in Sydney compared to the other Australian cities. The culture in the office of "accepting crazy travel times to get into work" was insane.
In my experience, I found renting to be much more expensive in Melbourne compared to Sydney.
This may be driven by affluent areas such as Rose and Watsons Bay.
So while these new measures could potentially lower pricing in the housing market for buyers, I could see this having negative affects for the renting community.
There may be a subjective element in being present in Melbourne while rent prices took off which makes Melbourne seem to have become more expensive, but it's not even close.
Edit: for instance, I live within walking distance of Melbourne cbd in a modern 2 bedder with 1 car space. Market rent approx $650 - $750 pw (not even including aberrations like docklands). In Sydney, you have to draw a substantially wider radius and transport time around the city centre and employment hub before you start hitting comparable properties and rates.
https://www.bedssi.com/rental-price-guide-for-australian-cit...
I did find that Sydney had more availability and options (at least during the market period I was searching). Lower Supply and High Demand should drive up Melbourne's price, but as you said, real estate in Sydneys CBD is just more valuable than Melbourne.
In London you quite often have the same issue, and that's a city with excellent public transport coverage (albeit a much more populous city). I have a friend who lives only 5 miles from where I used to live, and transport between our places often involved 2-3 changes, and could easily take 1.5 hours.
It's interesting you cited Melbourne, as I think it's the Aussie city generally considered as having the best public transport.
Where Melbourne struggles is the services as you get out of the inner suburbs. Where the bus services can be a 10 min walk, don't run often enough which is then compounded by them running late so often it forces you to catch an earlier bus because you'll miss your train half the time. So you end up trying to catch a bus that's 20 mins earlier than what you need it to be if you could depend on it being timely. Which means you have to leave the house half an hour earlier than if you just drove to the station.
However if you drive to the station most don't have sufficient parking. So if you aren't there by 6:30-7:00 am you can't get a park.
If you're heading to the city then once you are at the station it isn't so bad. Unless you're on a line where there are no seats and can be forced to stand squished up against a bunch of people for 45 mins.
But where the REAL pain is, is Melbourne's rail system is designed solely to get people in and out of the city. There is no outer loop. Meaning if you are in an say an eastern suburb and want to get to a south eastern suburb it requires going all the way into the city then back out again of a south eastern line.
Take the trip from the eastern suburb Ringwood to the south eastern suburb Clayton. A non peak driving trip would take 30-35 minutes. A train trip, not including the time it takes to get to the train station is triple that. Even in peak times when you can get express trains and driving is congested it's still going to be faster to drive.