To my knowledge, there aren't any North American spiders that would cause a "seconds count" type threat to your life. I suspect the way this normally works today is:

  Black Widow: Have a painful bite on the house!
  User: "Ouch!"  *slap*

  [one hour later]

  User: "Oh my god, I am in unimaginable pain."
  * User is driven to the hospital.

Or

  Brown Recluse: Have a painful bite on the house!
  User: "Ouch!"  *slap*

  [several hours later]

  User: This is starting to swell rather
        disturbingly, and smarts quite a bit.
  * User drives to their doctor

With snakes it's probably another mater. If a snake I could not identify bit me, I would be calling 911 first, and taking pictures afterwards before the ambulance arrived. If it's not a snake that I recognize as safe, then I wouldn't be taking the risk that it wasn't a venomous pet that escaped (since I can recognize the venomous snakes native to my region).

Identifying (or capturing!) the venomous spider or snake that bit you can mean the difference between them identifying the right antivenom or not. So, yes, surviving the trip to the ER is unaffected, but it might mean the difference between losing a life, a limb, or not.

The OP was indicating taking a picture of the spider then having the Amazon phone tell you if its a dangerous spider, then deciding on whether to rush to the ER or not. Sure take a picture of it and get it checked out, but this use case for this feature is a bit over the top.

That isn't even remotely true.

Many venoms have large delays, days even sometimes.

Which is why you should go to the ER or Doctor regardless