Can I set up a Sonos Amp with no wifi?

Wifi is required, because you can only do the setup via the Sonos app, which is WiFi only.

Additionally, the controller can not be run on the same device providing the hotspot. 

Wow...that’s a tremendous disappointment considering the price of the units.

Does this also mean that if wifi drops out, then the Amp cannot be used once set-up?

Perhaps you may want to better define your terms between external internet and LAN. If it’s set up using a Wi-Fi connection to external internet first, it will continue to play local music (on a HD or NAS) or TV sources,  as long as it’s on a LAN. However, it can not stream music from the outside world if it has no connection to it. 

Why should the price of the Amp say anything about the need for an internet connection for set up?

Granted, I’m new to A/V and am picking up the pieces from an A/V contractor that left in the middle of a job...but yes, it’s surprising that while I can bluetooth connect my phone and stream audio via my phone through say, a vehicles speakers or a cheap bluetooth speaker without a network no problem - I can also purchase a premium home audio product without that capability, even if the speakers are hardwired to the Amp if I understand correctly.

Seems like a major R&D oversight if the technology would allow it...but what do I know, I’m just a consumer.

It’s a network based system. From the get go. 

Since the Amp meant to be used with an internet connection, for most people this is not a problem - they buy the system for exactly this: playing Spotify or Apple Music. And, as explained above, using two phones you can set the system up.

Regardless of what the consumer assumes, the requirements are spelled out rather clearly.  As to what the consumer thinks being the standard by which a company operates, have you ever worked retail?  Because if you did, you’d know making the consumer’s wishes and assumptions the forefront of a business plan is the very worst thing you can do.  

Ask me about the woman who wanted a pint of half and half with a 4 month expiration date because “I’m going to Florida for 4 months and want cream for my coffee when I come back.” Or the guy who tried to return a Craftsman shovel to a store that didn’t sell Craftsman.  Or shovels.  Or tools.  Or any hardware at all.