It's really very reliable when setup right.
You said: "to configure the ATA, it takes a couple of minutes but it's very straightforward" but that's not true if you want you phone to always be able to get calls as you discovered. It took me 2 weeks of trial and error to get my phone setup so it works all the time. Yes it only takes a couple of minutes to initially configure it to call out but getting it to always receive takes a lot of trial and error. The problem is my phone has 3 screens of settings to configure with some values going from 0 to 20 million but they don't have any information on what settings to use so it works with their system. I emailed them about that shortcoming several times but they didn't seem interested in fixing it and putting up some examples of sample settings that work so I had to figure it out myself. I'm using an Aastra phone that has more settings to configure than a linksys ATA but it's still a problem even with simpler devices. Once everything is configured reliability is very good and voice quality is as good or better than a regular phone. The cost is very low, I only paid $2 for the phone at a swapmeet and $25 to get started. I agree the website is very slow though.
My comment was for the Linksys with Mango's instructions, but yes depending on the ATA/IP phone, etc., and many other variables it can become tricky. For example, some people will have to change their router settings, and most people will have some research to do online to figure it out.
However, this is true with most voip providers that do not provide a router.