The infinity of universes in which you can exist is reduced to a lesser infinity by the reverse time travel, since you could only have travelled backwards from universal states in which those specific conditions still existed, ergo reality appears to the traveller to be self healing.
That’s one of the things about MWI that is irritating, even though it still seems the most likely to me. It covers the testing parameters so completely that it is impossible to test. You always end up in a lesser infinity, but an infinity nonetheless. What we need is a way to quantify randomness in such a way that we might detect a change in the dimensions of infinities or something, but that seems improbable at best.