Ok, so I (think I) agree with you that the following poperties make it compelling to test/develop/refactor code: purity / statelessness, algebraic properties of programs (transforms…), high level (brevity).

Where I (think I) disagree, is that I think methodology stays globally the same: I would even say that it desn't throw away TDD but gives tools to reinforce it. FP removes whole classes of nasty bugs and so it makes you test more essential stuff ; secondly the tools help you more because the compiler and the testing library know more, so for example in Haskell statistical tests are easy to write, pervasive, and often very meaningfull.