Lumium, Mana Infused, Signalum and Enderium Plates don't have a recipe in the cutting machine. Mana Infused Plates can't even be made in the compressor.

It is possible this was an oversight, but I want to determine if there's a reason why Damien had the Thermal Expansion plates treated differently.

Sometimes there's a good reason that isn't obvious. It may be for example that he wanted certain things locked behind compactors.

I do recall that there used to be more materials you could only process exclusively in compressors or compactors, which I added cross-compatibility for in the 1.2.1 fix zip.

I believe this is an oversight, at least in regards to Lumium, Signalum , Fluxed Electrum and Enderium plates. Those should be added to the cutting machine for sure, especially because you can use a compressor and just skip the compactor which makes the point of that invalid.

The only thing I see that is gated behind having the Compactor specifically is the Gearworking Die (requiring Manasteel plates), which in turn gates the Phytogenic Insolator, Lumium, Signalum and Enderium gears, and 2 tiers of Fluxbore. Notably, despite being a tier or several tiers above the previous, you can use gear molds in the Fluid Solidifer for regular Draconium, but then Awakened Draconium gears again become gated by the Gearworking Die which is pretty strange.

edit: forgot fluxed electrum blocks

Gating the Gearworking Die behind the compactor doesn't seem to make that much sense since there is nothing you can do with it without a compactor.

It's not really "gated", it's just the standard progression of the mod. Even though the normal (non-omni) recipe is different, you still have to use the compactor to make the plates assuming no other mods are installed.