I think an argument could be made that they have left subtle visible effects, and we just haven't been able to reach consensus that that's what it is, and one of these days we're going to correlate the universe's contents, and when we do, we're going to be a bit upset. We don't seem to be sure what the deal was with oumuamua, and we're constantly getting reports of what look like alien probes on earth, but we (at least, whatever epistemic network I'm in) can only shrug and say "These things usually aren't aliens."

Yes, it is a good point that based on UDT one could ignore BBs. But it looks like that cosmologists try to use the type of experiences that an observer has to deduce either he is BB or not. Cosmologists assume that BB has very random experience, and that their current experience is not very random. (I find both claims weak.) They conclude that as their current observations are not random, they are not BBs, and thus BBs are not dominating type of the observers. There are several flaws in this logic, one of of them is that a BB can't make a coherent conclusions if its experiences are random or not. Also, even if there are worlds, with Big Rip and another with Heat Death with many BBs, SIA favors the heat death world. However, some BBs could last longer than just one observer-moment and they could have time to think about the type of experience they have. Such BBs more likely to find themselves in the empty universe than in the one full of stars. Also, interesting thing is that some BBs could appear even in Big Rip scenarios by the process called "nucleation", where they jump out of cosmological horizon of the accelerating universe. So, my point is that the idea of the heat death of the universe is getting more alternatives after the discovery of the dark energy, and there are some new arguments against it like the ones based on BBs. All this is not enough to conclude now which form of the end on the universe is more probable.