No, this doesn’t sound correct. In a normal ‘bonded’ setup, the Amp connects to the Arc using a 5Ghz channel created by the Arc, and not across the Ethernet cable. 

Is it possible that there is something close to either the Arc or the Amp that is causing wifi interference ? Are the devices close enough for a 5Ghz signal to reach?

I would also recommend that you submit a system diagnostic, and call Sonos Support to discuss it, or post the diagnostic number here for a Community Moderator to pick up. If there is a hardware issue in either device, it’s likely to show up in that data.

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.

When you speak directly to the phone folks, there are more options available beyond just the diagnostic analysis.

Did you turn WiFi off on the Arc?  It needs to be on.