I want my gravel(and CX) bikes to ride mostly like road bikes, but with wider tires appropriate for gravel. Sure, I like the additional flex and "compliance" that a carbon bar (and frameset) offers - but this applies to road bikes as well. To me, the main selling point of gravel bikes is that they're good for longer paved road rides AND good for gravel roads and tamer single tracks.
Suspension is going way too far into the off-road end of the spectrum for me - and in those situations I have very little use for drop bars. I'd much rather run 40mm tires on a flat bar XC MTB, than run a suspension fork on a drop bar bike. I'm also not doing mega long endurance gravel races.
If suspension didn't add any weight and could easily be locked out or adjusted on the fly to different riding conditions (i.e. electronically controlled/magnetic dampers) - I might feel differently. I definitely don't want a traditional fork suspension on my gravel bike though.