If it ain't better than a FPGA + D/A then it's not worthwhile. Said combination can also do filters in the digital domain. And at that point the Amiga custom chip loose.
Depends. Filters are tricky beasts that impose their own particular character on a sound, and they're rarely identical just for having the same basic specs. The 12db/oct. low-pass filters in my Matrix-6, my JX-10, and my MS-20 Mini don't sound at all the same, even when you don't have the resonance cranked up. Nothing in all the world but a Moog filter sounds like a Moog filter (except for the various naked clones of the Moog filter that were kiboshed for patent infringement!) It's probably possible to come up with a good emulation of the Amiga's filter, but it's not as simple as just "oh, digital filter, 12db, done."
Sure, but all 8bit samples, regardless of hardware, will sound like that.
Yes, but again, it's only one part of the equation.
Well, I'm not using AHI (don't have it installed), and play CD audio back with Hippo player. The only non-standard thing here is the playback rate of 44Khz (using a 31Khz screen mode). It's still Paula playing a few samples with DMA however (and Paula can go much faster than DMA), so I'm still not convinced 
Well, you're still circumventing the 8-bit aspect, and you're also doing playback at 44KHz instead of
x-28KHz, both of which bring the sound much closer in line with modern specs. Of
course that's gonna sound different than a game playing back 8-bit samples at varying, sub-28KHz rates.
Understand, I'm not saying that the Amiga can
only do oldschool-type sounds - I'm just saying that what we may generally think of as the "Amiga sound" has a lot to do with the way it was originally designed to be used, whatever clever workarounds we've come up with since then.
Perhaps it has something to do with it. My Amiga is connected to an amp with reasonable headphones, and when I listen to CD audio, I just hear sound that sounds almost the same as what my peecee produces. Back in the day they used to say the Amiga has CD quality sound. Turns out to be almost true.
Anyway, you've gotta use an amp with proper speakers or phones for your Amiga. Those internal monitor speakers do the thing justice 
Oh, I have run mine through proper speakers, and it's plenty nice. I just find that, for classic games and vintage MOD playback at least, I kinda like the things that are done to the sound by the 1084. It sounds right, to me.