Taygra dance shoes that look like Vans https://www.taygra.shoes/products/urbano-floral-grey 

Very fast/spinny (faster then Taygra Corrida) in their final form, but it takes them maybe a week or two of wear to achieve the final form. The mechanism behind that is that the outer edge of the outsole is rubber-ey and so it'll grip the floor. But after a bit of use it gets worn down and so the main plastic part of the outsole is what in contact with the floor thereafter.

Here is a picture of my outsole with worn-down edges:

This also suggests you can accelerate the process of the shoes becoming faster with a measured application of the file to the edges, but I haven't tried that!

Are they washable 

Other Taygra models (e.g. Corrida) boast being machine-washable, the Urbano didn't seem to like being washed as much (it seems there is a paper involved in construction somewhere, & I found chunks of paper falling out of them after washing them). They didn't fall apart, but clearly some structure within them didn't survive being washed.