You most certainly can have them all. If Civ 5 with Gods and Kings could do it then there is no reason why it is not possible. I would rather not have new civs if it means getting the regular civs. I think most of the new civs are unneccesary. I have no desire even playing against the likes of Brazil, Poland, Australia, Canada, Mapuche, Cree and Hungary, never mind playing as them. I would rather see them added later after the regular civs have been added or not at all.
I'm not a big fan of Civ VI's push for novelty for the sake of novelty, but there's no way I can see them including 50+ civs in the game - the fact that we already have more than Civ V did is as good a sign as the feature bloat of Civ VI in its current form that a third expansion isn't really feasible. I still don't know why people so widely assume there will be no DLC civs - expansions aren't just a vehicle for adding excess civs.
No Civ game has ever had complete overlap with a previous one other than Civ I. At this point the only missing 'regulars' (more than one past Civ game) are:
Babylon (Civs I-V)
Byzantium (Civs III-V)
Celts (Civ II-V, essentially replaced by Scotland)
Ethiopia (Civ IV, Civ V)
Iroquois (Civ III, Civ V. Replaced by the Cree)
Austria (Civ V, technically Civ III)
Maya (Civ III-V)
Portugal (Civ III-V)
"Vikings" have been replaced by Norway and Carthage by "Phoenicia". The Ottomans and Inca are in Gathering Storm.
Only one of those predates Civ III, discounting the Celts who've been replaced, two have substitutes in the game, and Austria isn't widely seen as a series regular anyway as it was a 'hidden level' cheat code civ in Civ III. It's not ideal that we're missing such significant civs as Byzantium, Portugal, Ethiopia, Maya and above all Babylon. Nevertheless they've managed to do pretty well at covering most of the major series regulars, adding some new civs, turning multiple Civ IV and V civs into new regulars (Polynesia/Maori, Indonesia, Poland, Brazil, Khmer, Sweden, Mali) and one or two of the all-new ones even deserve representation on historical grounds (Nubia, Kongo) rather than just because they're in a bit of the map they haven't used before.
All things considered, they've done a better job than many - me included - have usually credited them with, and it's not as though Civs IV and V didn't have duds no one's going to miss ("Native Americans", Holy Roman Empire, Huns).
There are Civ VI civs I don't like seeing on the roster that to my mind have earned their place on the basis of music or animations (Australia) or doing something mechanically unusual (Cree), just as I grew to like the Huns and Polynesia in Civ V, for all that there are duds like Georgia and Mapuche that score low on both criteria, and Macedon which simply shouldn't exist in the same game as Greece for the same reason as HRE and Germany in Civ IV. Neither of the Gathering Storm civs we've seen is deserving of a Civ spot on 'traditional' criteria, but both look interesting to play.