The example in the original post is actually a good case study for why trajectory planning alone breaks down. By the time the aircraft are on a predictable collision course with each other, you've lost 10+ seconds of potential remediation time that you would've had if you detected the error when it was spoken. Those 10 seconds really matter in our airspace.
ADS-B helps with this as it's self-reporting. And systems like ASDE-X are useful to track objects once they hit the ground. But low-altitude deconfliction is a big problem.
One problem for sure is that when you're close to the ground you have to be careful about buildings, cell towers, etc. Terrain is one thing, but when you're a few hundred feet AGL, you could quickly be in the way of tall structures if a TCAS alert goes off.
(By the way, I believe EGPWS would take priority over TCAS anyway.)