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Reconstruction filters in DACs are analog low-pass filters. They don't do a linear interpolation between samples.

You explicitly said a 6 kHz sine wave. Which is pretty much the textbook example of a waveform and frequency which would work perfectly.

Maybe you wanted to say square wave?

If I'm understanding you correctly, you're saying that while a perfect sinc interpolation reconstruction would allow you to capture up to 44.1/2 kHz, in practice since we're limited to FIR reconstruction filters we can't actually get that high? If so it seems like a fair point, although I'd imagine they'd be better than 6khz?

There's also the issue of the input signal not being band-limited which is necessarily true for real world signals given that you sample for a finite duration.

Input signals are ALWAYS band limited for digital systems. If you don't do this and you work for any company designing such circuitry, you'd be fired.

There's no such thing as a finite support band-limited signal.