are NET Switches worth considering?

@gkelly good idea! 

Silent Angel makes nice audiophile switches and linear power supplies to go with them:

https://silentangel.com/n8/

English Electric (a Chord company) makes well-regarded switches, too:

https://englishelectric.uk/8-switch/

I think both would be about $750 USD.

I use the Silent Angel Bonn N8 with a Forester F1 linear power supply with my Innuos Zen Mini Mark III and McIntosh DAC2 (in a MA8950), with Shunyata Gamma cables. The Silent Angel switch and LPS made a nice improvement when it was added.

Is a switch useful if the only ethernet cables connected to the router are the server and streamer?

+1 +1, I use the LHY-SW10. Absolutely worthy purchase but if you go there, you should go further. You can see how it is incorporated in my system with a pretty full list of equipment.

Only possible reason to do it is if your existing streamer and dac are not filtering out noise coming from your ethernet connection.  The current Stereophile (Brilliant Corners column) has a brief mention of an extremely cost effective solution: TP-Link MC220L ethernet to fiber converters, TP-Link TL-FM311 SFP modules, and a short run of fiber optic cable.  

Another option, a little more expensive, is to just get same basic setup through Small Green Computer:

Systemoptique