I’ve worked in motion picture auditorium sound and have experimented with this, as well as done quite a bit of reading.
You can use a "phantom" channel, but, a center may sound better. The reasons is related to your head and how it affects sounds from different locations. (Look up HRTF). I actually used to advocate for never using a center at home until I tried it. :)
With music and stereo speakers, pay close attention to instruments and how they sound as they are hard to the sides and in the center. Ever notice they sound more vibrant on the sides, and more laid back in the center?
Having an actual center source fixes this which really can help dialogue intelligibility and transparency. Also, the Neo6 music modes are pretty damn outstanding in filling in the center of even very good 2 way systems for the same reason. I think more music lovers should try this. This may be related to why 3 channels were often used in classical recordings way back when.
Another reason is the center channel improves off-axis localization. If you really only listen in front of the TV this may not matter.
I’d say it’s a moderate improvement though, not a must have.
You may want to look at the sales at PartsConnexion. They routinely have several center channel speakers on discount.
https://www.partsconnexion.com/eblast/2018/may-jn/ss053118.html
Best,
E