Actually, it is. It often doesn't rain for hours on end, so people work a bit longer or start a bit earlier to avoid the rain. Otherwise, there's umbrellas, ponchos and plain old acceptance of the fact that you will be a bit wet for an hour. My dad used to say when it was pouring: "You're not made out of sugar, are you?"
And yes, public transport is busier on some days than on others, is that a problem? How is that any different from motorists on roads?
I highly doubt that, it speaks completely against my lifelong experience as a cyclists. The vast majority of all people are fair weathered cyclists and bike lanes are mostly empty half of the year.
You get cold, wet and uncomfortable, and have to be very flexible with time. Even if you can "deal with it", it's still very real negative aspects, and why would you put up with that if you don't have to?
My point is that you have to have full capacity public transport anyway so the bike lanes are really redundant, a "nicety" and as such I think they should have little space and low priority, it makes perfect sense.
Why don't we have skateboarding lanes? Running lanes? Horseback riding lanes? It's fun, it's healthy, it's good for the environment! Because it's impractical, slow and inefficient, just like cycling is.