[drpossum]

That doesn't validate your assertion that particles are just "an approximation". Just because it's used in perturbation theory doesn't mean it's exclusive to it.

You're also manifestly wrong on "the free particle is the only system we can exactly solve".

[DiogenesKynikos]

Okay, it's not "the only" system we can exactly solve, but it's 99% of what we solve in practice, and it's the exact solution you'll see over and over again in QFT 1.

The free particle solution is an approximation to reality, because reality includes interactions. There's a mathematical formalism to this that we'd agree on, but you might disagree about how to describe it in words.