...with ensigns fanning them with giant feathers. And any time the captain is bored, they can order two redshirts to fight to the death.
It had nothing to do with that. The bridge design was driven by the pre-production plans for Voyager, which got watered down by UPN. The show as originally going to feature a more explicit focus on the idea that the Voyager crew was half Starfleet and half Maquis and only by uneasily working together could they make it back to the Alpha Quadrant. The side by side chairs of Voyager are in service to that concept - Janeway was the captain, but her and Chakotay were each informal leaders of half the ship. For no other reason are there two chairs than that: the intent to show via leadership that the two crews were working together (or not). The plan was shoved away. Voyager did only a about a dozen Starfleet-Maquis "tension" shows across 7 seasons. Most of the Maquis became capable and obedient Starfleet officers or crewman within a few episodes. Chakotay was pushed more to the background starting in Season 3, and then even more so when Seven of Nine was introduced. The driving force behind this was Berman's insistence on Voyager being episodic rather than serialized, and most of all, UPN's insistence that Voyager be, more or less, TNG 2.0. The show pitched to UPN was not the show UPN asked for every season. If UPN could have continued TNG, they would have. The dual chairs are therefore a relic of one of Voyager's many "what could have beens" as an ambitious premise was replaced by a very safe product. For what it's worth, the same thing happened with Enterprise. Berman and Braga had one vision, UPN had another, and UPN largely got its way.
The other issue to consider, of course, is – if Chakotay doesn't sit next to Janeway, then where exactly does he sit? Does he just stand at the tiny central console like Seven of Nine started to do, always looming over Janeway like a spectre at the feast? Have Tuvok, Paris, or Kim scoot over and pull up a second seat at their respective stations? Stick him at one of those seldom-seen stations at the front of the bridge on either side?
I think that very question, and the two chairs we got all comes down to Voyager's original concept being altered into a kinda TNG 2.0 during pre-production (and even more so during the series). The first officer of the ship being a distinct command division position has one origin and one origin only: the plan for Star Trek Phase II that was repackaged into the basis for TNG after Star Trek IV was a big success. Remember, Riker is Decker, Troi is Illa, etc. Funny enough the Decker we saw in TMP had no seat, but his TNG version in Riker did right in the middle, along with the ships therapist (the most 80s thing ever). That role in the show also likely only existed so a younger actor could fulfil the "action hero" and "ladies man" role that an older (but by no means old) Kirk/Shatner wouldn't fill in Phase 2. With Picard in TNG, it made sense. But that's why it was there. DS9's first officer made loads of sense: the top Bajoran on the Bajoran station who was actively shown being, more or less, the chief operating officer of the starbase. But Voyager? At one point, yeah it was because of the Maquis thing, but when the TNG-ination of the show took root, I really think it was just because TNG had a first officer job, and thus a seat. Voyager would be a completely different show without chakotay, but it seems like these are the reasons. And sure enough, the next show they did, Enterprise, folded the first officer back into another character and eliminated the second seat. Bigger picture, Voyager and TNG's bridges are quite different and had their strengths and weaknesses to them. The brilliance of the TNG bridge was its height, actually having the 3 seats in the middle, and Worf behind on the railing, because it allowed just great cinematography like this: So many character scenes in TNG was shot from that angle. It could also show the entire bridge at once with all the leads, which it often did. It's weakness though was after the departure of Wesley Crusher, the Conn seat was always fixed by an extra. Voyager fixed that problem by making the Conn officer a principal character (Paris) for the entire series. But it arguably created another problem in that the spread of the bridge meant that Tactical and Ops couldn't be in the same shot, TNG style. You couldn't do frames like the shot above really easily, but the bridge did darkness a lot better than the TNG bridge did. Frankly, in the Star Trek mode of storytelling, I'm not sure in this case there was any other solution than to have the Captain and First Officer sitting side by side. Looking over to Battlestar Galactica, for example, which also had an explicit First Officer (Tigh), he and Adama did their scenes across a situation table. Pretty much the same dramatic tool.