Downsides of 3-terminal capacitors and LC filters for power supply to IC
The big- value feedthroughs are useful to knock down high-frequency noise, so you could possibly get rid of the PI filter.

Next to the device, the big benefit of FT caps is their low ESL at a given value. You can replace multiple 0.1uF with one 1uF for example. So they can save space under a large device that needs a lot of bypass.

For these reasons FT caps are starting to show up in mobile phones as their main application. With that volume driving them it’s not such a concern sourcing them.

There is close cousin called the XY cap that has 4 terminals. It’s more expensive, is patented, and has relatively few sources. It’s debatable whether it’s better than the FT.

That all said, with the relatively low frequency you’re using you probably won’t see a benefit using FT caps. You can get by with conventional caps and a ferrite bead, like 4.7uf + 600 ohm + several 0.1uF.  If improved PSRR is needed consider a separate LDO for the ADC.