I have a Pixel 2. I can confirm that they no longer receive updates.
I have bought refurb phones from woot. I can confirm they brick from OTAs within 30 days and you get zero support from woot or google for your money. 
Just stick to shirts.
I bought one of these for my oldest kid about six months ago. It functioned fine out of the box, but the battery life on this model is absolutely horrible. It would only go about 3-4 hours with regular usage. He was pretty much tethered to a USB charging pack everywhere he went.
No SD slot? Pass
Unfortunately with everyone wanting (apparently) their phone to be “water proof” as the #1 new feature they HAVE to have, openings to the outside world are being eliminated. First they all eliminated replaceable batteries because they claimed there was no way to seal the battery chamber (though somehow my TIMEX watch has an easily replaceable battery and is water proof to 50 METERS!) and eliminated most buttons for “additional screen space”. Then they went after Memory slots (though with more usage of cloud storage that is not an issue for the majority who trust that route) and of course the 3.5mm (or any other size) audio / headset jacks are all gone now too (Bluetooth or Wi-Fi for headsets / speakers or just do without).
I don’t like it either, but in the communication device industry the trend is less ability to directly connect to the outside world and charging higher and higher prices for that loss of privilege…
If you could actually rely on Bluetooth / Wi-Fi / Cloud Access to not fail at a critical moment and not be hacked into so easily it would be OK. But then how could they sell all those add-on safety, security and storage plans (which of course are now annual or monthly subscriptions)?
And of course how do they force you to buy a new phone? All the major carriers simply stop supporting a few hundred models of devices every year. Upgrade or do without.
Wow, that turned into a longish rant…
I bought a Pixel 2XL on Woot last year and have had zero problems. Battery is great, the photos are amazing. You can’t go wrong for $99.
This has happened to exactly zero of the several refurb’d smartphones I’ve purchased from Woot over the years. If you spent half a second to think about it you’d realize that there’s nothing special about buying a refurbished phone sold by Woot (and refurbished by someone else, obviously) that would “brick” them from OTA updates. In fact, I’ve never had any mobile device fail an update, ever.
You just got unlucky, apparently, but there’s something else fishy about your story because if it did indeed fail “within 30 days,” well, obviously you’re within any warranty period (which, in this case, is 90 days for these phone refurbs) and are due a refund or replacement. Every time I’ve had an issue and contacted Woot CS they’ve resolved it. So I’d go as far as to say you’re making the whole story up (especially considering your wording implies that this has happened to multiple devices, which is incredibly improbable,) but at best you had an actual problem and just didn’t bother to contact CS so you could complain about it on this forum.
Google’s devices in particular don’t have any removable storage, and this is hardly news. I can’t think of any Pixel or Nexus phones or tablets that have SD card slots, and this goes back several years. Also, Apple seems to feel the same way about removable storage!
I’ve purchased multiple “refurbished”/S&D PIxels from Woot, and they generally come in decent shape. They’re clearly in “used” condition, likely trade-ins, with the expected scuffs and scrapes. I bought one Pixel that definitely has a quite heavily-cycled battery and a couple hardware issues, but at $50 for a backup device I can’t complain too much. The company that does the “refurbishing” clearly doesn’t do much other than erase the device if necessary and maybe wipe them down, but if you want to take a chance on a cheap used device these are worth a shot.
One thing to note is that, of the Pixel series, the 2 XL is the one with all the display issues, so if I could suggest avoiding any of them, that would be the one. The rest might have their quirks but the 2 XL is probably the most troublesome. The original Pixels from 2016 are still viable, and although they no longer receive updates they max out at Android 10 which is still very usable. The Pixel 2 (non-XL, obviously) gets Android 11 and no further updates, but has some hardware upgrades over its predecessor that make the $60/70 (64/128 GB) offering for sale here quite compelling (and if you get one that’s not in great shape, just contact Woot CS to return/replace it.) If you want something that’s still receiving updates, the Pixel 3/XL have been on sale as refurbs here recently in the $150 range, and they’re still supported through October of this year, and should max out at Android 12 if I’m not mistaken.
Holy 
someone has been triggered.
You can learn a lot from a no-holds-barred wordy discussion. “Avoid the 2XL” (display issues) and “no memory card slot” (they kinda have to still have a sim-card slot, right). No more support planned (past some point soon) but will be able to load stuff-in-general. “Your mileage may vary” for battery and/or general remaining lifetime and functionality… enough and more.
Considering repurposing as a smart remote for my devices and smart/wifi connected things around the home. Worth it?
The lack of a micro SD card slot isn’t a dealbreaker unless 64 or 128 GB of internal storage isn’t enough, and/or you absolutely need to be able to add an SD card for some specific reason.
The Pixel 2 is no longer being updated as of last year, but it will of course still work until the final OS version isn’t enough for the apps you want to run on it (likely at some distant point in the future.)
An old phone like this would definitely work for that, but you could find a much cheaper/older phone to do the same thing (e.g. a prepaid “burner” phone, a used one from eBay, something from a device recycler that resells trade-ins, etc.)