I said it is inherently problematic, not exactly that it's infeasible.
The Netherlands is excellent support for my claim because of what you just said. The cities support less car traffic and slower driving speeds. Something has to give and in that case its drivability. In fact there are a lot more streets where cars can't go at all, or are just mostly bikes correct?
And the 3 modes/lanes in one place is still not even solved while minimizing cars. Cyclist are more than 1/3rd of Dutch road deaths and the Fietsersbond has even argued that the middle lane. https://swov.nl/sites/default/files/bestanden/downloads/FS%2...
Let's say you have space for two lanes. You can either a) install two car lanes, so >95% of people drive, or b) install one car lane and one bike lane, so 75% of people cycle. Which one is more drivable? Hint: it's the one with significantly fewer cars.
Similarly: car infrastructure takes up a lot of space. If your destination is 10% closer because cycling means far less car infrastructure is needed, you'll actually end up driving there faster.
A street's car traffic capacity is far less important than its total traffic capacity, and the last-mile driving speed is a rounding error on the whole trip. If you like driving, you should be in favor of building more bike infrastructure!
And yes but those road deaths are caused by cars. There's just more victims on bikes because there's so many bikes around.