Cell phones are available for free, from the government, and every phone I have ever received for free via Lifeline has had no problem with Blizzard authenticators, from the very first phone they gave me all the way up to the Moto G Pure I just received as a free upgrade.
Not being able to afford a plan on a big cell phone bill from Verizon, etc., is exactly why Lifeline exists. They only check income (not assets), and if you already have a social service program like Medicare or SNAP, you automatically qualify.
If that doesn’t work for you, there’s now also the ACP (affordable connectivity program) which gives qualifying applicants $30 a month off virtually any “broadband-speed” (4g or 5g) cell phone plan from any carrier. (Or home internet, or a wi-fi hotspot, or 4g/5g on your tablet… take your pick.)
Upon qualifying, ACP will give you a pseudo-credit-card number, which you input on your carrier’s website to apply your $30 every billing cycle. Whatever you spend over $30 is your total cost per cycle. My wife uses this program and pays nothing for her service. Only thing is, the ACP doesn’t generally get you free equipment, whereas the Lifeline program definitely does.
https://www.fcc.gov/general/lifeline-program-low-income-consumers
and
https://acpbenefit.org/