Sure, and I'm no expert on the subject, but when someone writes "a typical Li-ion battery" they mean the common rechargeable lithium battery with lithium cobalt

Sure, and I'm no expert on the subject, but when someone writes "a typical Li-ion battery" they mean the common rechargeable lithium battery with lithium cobalt oxide, not lithium iron phosphate. LiFePo4 is not a "typical" Li-ion chemistry yet, unfortunately.