The rubber wheel metros are mostly a result of lobbying by Michelin. They're an interesting curiosity, but I think there is a reason why they haven't really caught on outside of France...
And Michelin must have a phenomenal lobbying team if they managed this: https://en.wikipedia.org/wiki/Rubber-tyred_metro#List_of_sys... (In particular, "didn't catch on outside France" is, well, just plain wrong.)
The list once you exclude that basically consists of
* France, which wanted a niche technology to export and maintain supply domination over
* China, Japan, and Korea, trying to replicate it
* Quebec, which often looks to France for planning inspiration
* Mexico and Chile, which were recipients of French development assistance that included using French suppliers
What a silly assumption. They are not.
Replicate the industrial strategy, not the technology.
Railways are also part of this strategy. China, Japan and Korea all export railway products from high speed rail to subways to monorails, and so in this context rubber tired metros are another niche technology to get an edge in. Note that this strategy doesn't always work; no one outside of these countries is very interested in maglev trains, for example.
---
The other part of this is development finance. Countries that do not have know-how with big infrastructure projects often look to international institutions to build projects and secure financing. And part of the deal is that if you take French money you must spend it on French suppliers, and this is true for basically any country doing this kind of lending, so basically the lender is getting both interest payments and spending towards its economy. The Chinese and Japanese compete a lot for railway projects in particular; Japan built the Taiwanese HSR and the Hanoi and Ho Chi Minh City metros, China is currently building high speed rail in Thailand and Laos, etc.
Even in the countries where they exist, rubber tired metros are niche.
You can't retrofit rubber wheels easily so of course compared to all metros as a new technology it will be rare
Rubber tired metros are also a niche in new metros.
Retrofitting actually has some advantages for old lines with short station distances, tight curves and steep gradients, whereas new lines can be planned with the limitations of rail technology in mind.
And generally speaking 5 % wouldn't be considered very steep at all by modern standards. Gradients up to 4 or even 5 % weren't uncommon even on older rapid transit systems dating from a century ago, and for modern multiple units I'd regard 4 to 6 % as about par for the course.
And in hilly terrain, a number of systems definitively go beyond that into the 8 – 10 % range, including some new built systems (e.g. the light rail systems in Stuttgart, Tenerife and Jerusalem).
Unless you go with a rack railroad, or maybe a cable way, you are only climbing hills with rubber.
BART is standard steel track and steel wheel, just different wheel and rail profiles - plenty of resources if you wanna read about it
https://www.railwayage.com/news/bart-revised-wheel-profile-q...
The article you linked to talks about all the money that BART's thrown at the noise problem without addressing the elephant(s) in the room: BART cars are aluminum tubes that are inherently noisy and BART wears its tracks aggressively. The first iterations had carpeted floors which absorbed some of the noise, but those got predictably gross.
Much of the track noise comes from corrugation because the wheels are dragged over the track. Other systems might grease their wheels so that there's more slip in turns, BART can't. Other systems sand the tracks in wet weather so you don't skid, BART can't. Modern systems have anti-skid systems so that you don't wear the wheels. Bombardier's anti-skid system is awful. So the new cars flat spot the wheels at a much higher rate than the old and you get noisy track (and noisy trains as they thump thump thump down the track). BART grind the rails and the noise goes away for a bit, but it eventually comes back with a vengeance because they're doing everything they can to avoid addressing the underlying problems.
They are useful if stations are very near each other because of greater braking power, so you can stay decently fast in-between stations.
Lines 1, 4 and 14 have rubber tyres and platform doors because they are fully automated (or in the case of line 4 in the process of being fully automated). So far Paris only fully automates rubber tyres lines.
Line 13 has classic metal tyres and is only semi-automated, but it has platform doors because it is very high traffic. Most Parisians avoid line 13 at rush hours because it is probably the most packed line in the city.