I'm from Copenhagen. Almost two thirds of us use our bikes to get around. The weather is incredibly shifty on this island and during autumn and winter it rains pretty much every day. Not always all day, but there's a high chance it will rain during your daily commute.
So what do all the people here do? To cope with the weather we have developed advanced technology that negates the effects of rain. It's called: the raincoat.
That is a cultural dislike. Seriously.
I was born in the states - Indiana. NO one walked when it rained unless you were poor. When you did walk, you probably had an umbrella. Being female meant that sometimes, people would offer me rides randomly.
I moved to Trondheim, Norway. There is a saying here - "There is no bad weather, only bad clothes". Which, you know, is only half correct. I do not drive here. I walk. I take public transport. I do this regardless of whether in general. I do tend to avoid walking if it is really heavy rain, but not so much in normal rain. People bike with snow and ice on the ground (I'm not that brave). And yes, clothes make a big difference (though they do not turn weather 'good). You simply get used to it and get over it.
Unless forced to do differently, the most efficient choice is evident. I'm also lucky enough to live inside the city. Commuters that can't work from home have it even rougher, since they live outside and they take up to an hour or more with public transport.
But honestly, the bicycle is cultural as it would be better to prioritize bikes so it is faster. Same for public transportation. Car-first infrastructure and lack of pedestrian/bicycle/mass transit are political decisions.
They've had some for years, mind you - but they were really more in the tourist spots. Now they are putting them in next to a fair amount of regular bus stops.
As a resident of Milan, I find this rather displeasing. I don't own a car (and have no plans to own one), and I exclusively depend on the metro + trains to get to work, which is too far away for serious walking or even cycling. FTR: it's actually far easier to go there (at least from where I live) with public transport than walking , cycling, and even with a car.
Even at full capacity trains are already packed, and I'm afraid that this will make matters worse than before (example: at some point last month metro lines cut rides to < 50%, and were hastily pushed above that again because trains were too crowded even for the decreased ridership, people who could not work from home and had to go to work instead).
Also, what happens if it rains?