Is it possible to get that affordable rent within, say, a year? My understanding is the wait list for this affordable housing can stretch multiple years.
Maybe Vienna is affordable to people living there, but at the cost of extreme difficulty for outsiders (even Austrian outsiders) to move there.
So, if you grew up in a poor village with little economic opportunity, you will have a lot of difficulty moving to Vienna to open up your job prospects. The affordable housing there comes at the cost of denying outsiders an opportunity to better their position in life.
Is that better than riding rents displacing longer term residents? Maybe, I don't know, but there are invisible victims to many affordable housing schemes.
The free-market housing (and regulated market housing) still exist by the way, but the prices are way lower than they are in similar-sized European cities (because they compete with non-market housing), so yes to your question.
However I claim it didn’t really solve the problem, it just alleviated it - when I moved to Vienna in early 2005 finding an apartment was easy and the prices low enough that even as a (working) student I didn’t have any trouble paying for rent. You could have a good life in Vienna even earning minimum wage (I know because my part-time student job earned me less than a full-time minimum wage would have).
Today this is no longer possible - it’s not easy to get a cheap apartment and prices are higher to a degree that you need a considerably higher-paying job to lead a comfortable life and the biggest chunk of that change is due to increased housing costs.
Amsterdam, Paris, London etc have it even worse but the problem is life in Vienna used to be very affordable (not that long ago, even 15 years ago) and it’s a lot less so today.
The same can be said about Berlin, prices here are lower than Amsterdam et al but it’s still a lot higher (relative to wages) than it was 15+ years ago and the gap keeps increasing.
I used to live in Vienna for 8 years (2005-2013). Looking at https://www.immobilienscout24.at/regional/wien/wien/wohnung-... the prices per square meter are a lot higher than I paid at the time: the cheapest rentals I saw was just above €10/m^2 (rare) and more commonly were around €15-20/m^2. When we left in 2013 we were paying €480 per month for a 65m^2 apartment (that was already cheap at the time but is even more out of the ordinary today).
Anecdotally everyone I know in Vienna started complaining about housing unaffordability around the time we left (it was never a topic when I got there) & that seems to still be the case.