Why are there types A and B in ISO 14443?
I found a nice answer to my question here: http://www.secureidnews.com/news-item/is-the-debate-still-relevant-an-in-depth-look-at-iso-14443-and-its-competing-interface-types/

Short summary of the article:

The first interface was type A, supported by Mikron and their Mifare technology, later bought by Philips (NXP). Some limitations quickly occurred: the initial implementation was a memory card, and not a microprocessor card. At the time, type A couldn't power up a microprocessor continuously. The Innovatron company had working microprocessor cards, so their technology was integrated as type B in the standard. This separation is not relevant anymore since you can have type A or type B memory or microprocessor cards, and we ended up with two competing technologies in the same standard.

As a final note, on Figure 2 of the ISO 14443-2 we can see that newer and faster bit rates all use the type B modulation and coding (BPSK and NRZ-L). Maybe in an effort to phase out type A?