One of the reasons why I think that a megalomanic amount of metastable de Sitter vacua in string theory should not exist is that they have a megalomanic number of ways how they can decay.
That's how I started a text called Landscape decay channels in 2005 whose goal was, of course, nothing less than to nuke the landscape. Finally, people are beginning to look into it a little bit more seriously.
Figure 1: Percolation through sandstone rocks in the landscape ;-)
Today, Sash Sarangi, Gary Shiu, Benjamin Shlaer (SSS) and, in another paper, Henry Tye discuss resonance tunneling and DBI tunneling (emerging for string-height barriers) that are capable to enhance the tunneling rate under certain circumstances. And "finally [they] argue using basic ideas from percolation theory (including concepts from the renormalization group, emphasized in Tye's paper) that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels and discuss various cosmological implications" (SSS abstract).
These authors seem to justify exactly the outcome that I predicted: the eternal inflation becomes impossible, most of the vacua in the landscape are unpopulated, and the vacua with a small cosmological constant like ours have a higher chance to be populated because the effective number of non-collapsing decay channels is small for these vacua (SSS). Yes, if the mechanism is correct, then string theory solves the cosmological constant problem and string theory can easily generate exponentially small values of the cosmological constant (Henry Tye).
At any rate, physicists should read these two papers (SSS, Tye) and find other arguments whether this rapid tunneling exists or not.