Are you attempting surround sound?  How quickly do you expect the audio to switch from TV to TV?

Normally, ARC will be centered at the base of the TV. Obviously, in this sort of setup ARC cannot be centered with all TV’s unless they are stacked vertically.

Really just for sports so surround sound will only be for the center TV. Thanks!

You still have the problem of matrixing the three various ARC/eARC outputs into a single line to the speaker. 
 

I’d just as soon leave one connected at all times, and designate that one as driving the speaker, and have the other two be silent support.

What happens if you connect the ”left” and “right” tv’s to the centre one via hdmi cables? Then select hdmi1 or hdmi2 as the source on the centre tv when you want to watch and hear that one. Would that work? 

I wouldn’t think so, the TVs are not set up to receive/pass through ARC signals, only to generate them from within their CEC controller electronics. 

No, you cannot feed one TV to another via HDMI. CEC is control only, no video or audio can pass over CEC.

Yes, I know that you see similar approaches in bars. They’ve gone to a lot of expensive trouble and they are not using SONOS. The most practical approach at home is a conventional A/V receiver. Depending on the receiver, you may need one or two adapters to send TV audio to the receiver. There will be some control quirks, especially if you want Dolby Atmos for the center TV. Maybe you could work around most  of the control quirks if you use a CEC blocker in the center TV HDMI-ARC connection to the receiver. If control is really quirky, you may not be able to use the HDMI-ARC connection between TV and receiver. You’ll need to experiment.

Potentially all 3 TVs on different channels, and you want to use one Sonos Arc and select sound from one of the TVs? What about using the optical connection, with a simple toslink switcher with remote?

I would go about this a different way.  Get 3 or more sources connected to an HDMI MATRIX with at least 3 outputs (one for each TV).  Connect the Arc to the main TV only.   So instead of just switching the audio only, switch both audio and video from one of the non-primary TVs to the primary TV.  Since you’re planning on using identical TVs, with the same video characteristics, a fairly simple HDMI matrix will be fine.

If you’re really need to have the audio match the video from the non-pirmary TVs, that I would get something like the HD Fury Arcana along with a HDMI matrx that has 4 HDMI outputs.  3 of those will be for the TVs and 1 will connect to the Arcana which feeds the Arc (You may also need to connect Arcana to a TV for EDID reasons, not sure on that).  So now your matrix will control what content is sent to your TVs and your Arc, with all of them playing the same or different sources as you wish.

Thanks Danny. That sounds like a good solution.