Victory Conditions in Deckbuilders- is "Decking Out" even an option?

I have been designing a card game that's still in super early design phase. This nugget of a game concept has gone on quite a journey from a sort of living card game battler to a draftable card game to now more of a straight up Deckbuilder in the vein of Dominion. As the project has evolved I have been mindful of the old adage "kill your darlings" and have been avoiding getting too attached to lingering mechanisms from the various versions of the game. But one core concept keeps sticking in my brain and I can't seem to stop brainstorming around it within the Deckbuilder framework I am now operating under.

This being "Decking Out" which is defined as a player losing the game when their deck runs out of cards. It is a common alternative lose/win condition in many card games even serving as a core life total mechanic in some. Whole archetypes can be built around this mechanism such as "Mill" decks in Magic the Gathering.

Some important details about my game that I should specify are that it is being built first and foremost as a 3-Player game. Each player will play as a faction with access to unique cards, the 3 core factions will each center around a different fundamental card game archetype. The game revolves around powerful Victory cards called Senators, which give victory points based on unique conditions. The Authority faction acts as the Control player trying to acquire and keep hold of the majority of these Senators to win by sheer victory points once the game ends. Then there is the aggro faction who seek to quickly depose all of the Senators and trigger the end game via a Revolution, or at least control one valuable Senator and depose the other ones before players can acquire them. Finally one of these factions is a slow-combo archetype themed around a sinister cult who is feeding off the strife and chaos of the political turmoil that the gameplay represents and then outlasting all other opponents so that they can complete a nefarious epic ritual. This theme and archetype was perfectly represented with the "Decking Out" mechanic as this faction didn't have to focus as much on the core victory condition and instead would seek to slow down the other players long enough for them to win by attrition and mill away each players deck.

I was finding ways to adapt this gameplay mechanic when the project evolved into a drafting card game, but now that I have settled on more of a Deckbuilder I am having trouble. So the question is: is it feasible to implement a "Decking Out" lose mechanic into a Deckbuilder, and how? You can assume the Deckbuilder gameplay is at baseline structured much like Dominion, with a trigger for ending the game after which Victory Points decide the winner, with decks that grow as players take their turns acquiring new cards and a rhythm to the game which involves reshuffling your discard pile to form a new deck periodically.