If a system using Tails and Tor always connects to public wifi in a city far away from someone's home IP address, what are all the different ways this would backfire such that authorities still manage to pin-point that person's identity or real hometown?
It is possible, but highly unlikely. No matter what steps are taken, true anonymity is never possible. If someone was running an illegal business, the authorities would eventually find them and arrest them. Nobody is ever completely anonymous and can be identified if there was enough effort into doing so. It takes just one vulnerability in an illegal website someone is hosting for them to be hacked an identified. This vulnerability depends on the situation though (and I don't know many since the authorities don't always say how they catch these hidden services). The Silk Road was supposedly taken down by a Captcha which leaked an IP address. If someone using Tor accidentally gave personal information, they would be exposed. If someone was buying a product, they are also at risk of their package being intercepted or their buyer revealing them or their buyer being someone who worked for or with law enforcement.
However, the normal privacy-minded user would most likely stay mostly anonymous with the setup in question and unless they are doing something illegal, they probably won't get indentified except if the Tor browser or Tails OS has some sort of vulnerability (unlikely, but possible) which a hacker could use to expose you. Or if you accidentally downloaded some sort of malware or spyware that modified your Operating System so much that Tails OS can't wipe this malware or spyware, though most Tor users are cautious enough not to. So other than getting hacked, I don't really know any way a normal user with your setup could be indentified. I mean it is always possible, but it really just depends on what the user is doing and what precautions are they taking and precautions they aren't taking.
List of Tor browser vulnerabilities in the past:
Discovered by: Zerodium
Tor Browser through 8.5.3 has an information exposure vulnerability. It allows remote attackers to detect the browser's language via vectors involving an IFRAME element, because text in that language is included in the title attribute of a LINK element for a non-HTML page. This is related to a behavior of Firefox before 68.
Tor Browser before 8.0.1 has an information exposure vulnerability. It allows remote attackers to detect the browser's UI locale by measuring a button width, even if the user has a "Don't send my language" setting.
Tor Browser on Windows before 8.0 allows remote attackers to bypass the intended anonymity feature and discover a client IP address. User interaction is required to trigger this vulnerability. Even the this does not apply for Tails OS, it just shows that the Tor browser is susceptible to hacks and snooping.
Basically, a lot of vulnerabilities of the Tor browser were those which existed in Firefox as the Tor browser is built on Firefox. Hackers and governments pounce on these vulnerabilities and use them to expose Tor browser users. It is thought that the government may have used the NoScript vulnerability according to: https://www.pcmag.com/news/tor-browser-has-a-flaw-that-governments-may-have-exploited.
Also as a sidenote, if the person is using Tor from a public area with a security camera, the authorities can view the footage and find out the physical appearance fo the user making it possible to pinpoint their identity.
So to answer your question, it's very unlikely that your identity could be found or your hometown, especially if you aren't doing anything illegal. However, the atuhorities can still find you if the Tor browser or Tails OS has a vulnerability (where the authorities can use to gain access to your device), you download some sort of extremely hard to remove malware/spyware, or you are caught through a security camera.