Several times I have been in locations where tsunami risks are either actively signaled or self-evident. Lima where I am right now has long beaches dominated by cliffs with exit routes about every km. Hiking the West Coast Trail in BC, Canada I have also been in situations where an extremely smooth cliff overlooks a low tide only trail. Leading to Tofino, Canada, you have a 40 km stretch of low lying lands before you see any higher ground. Depending on your location and how much advance warning you receive, you may not have the opportunity to reach higher ground in case of a tsunami warning.
If you have experience with big waves, near beaches, or especially near cliffs, you know that they are especially dangerous when they contact the shore. Both because that's when they break and because they can throw you against solid objects. In fact one of the best ways to safeguard yourself from a breaking wave is to dive under it, heading offshore (not something I suggest here, just an example of something very counterintuitive that works).
Looking at the videos shot of either the 2004 tsunami @ Phuket tsunami or the 2011 Tohuku, Japan earthquake the waves don't even look very big.
I know considerable effort since 2004 has been made to monitor for, and mitigate, tsunami risks. Has anyone looked into whether swimming a few hundred meters offshore and waiting out the main water disturbance would be a valid risk minimization strategy, if no timely route to safety was available?