Well ALL MEDICATION have half lives and NO they don't taper off by themselves, that's just silly.
PPL who don't like to start low dose and and get off cycle by tappering are usually super impatient, they Front Load mega doses and stop cold turkey to save cash, thats really stupid because you lose alot of gains when you stop cold turkey.
Infact i bet in HRT, people who get prescribed Testosterone they don't even do PCT they just tapper off slowly week by week and by default their body increases their natural production to meet normal stable levels slowly.
For example, someone who takes lets say an Anti Depressant Like Paxil and starts at mega dose, he will suffer greatly and if he quits cold turkey after months, he will basically shoot himself. Same principle applies for all meds, including testosterone which is a medication.
All the noobs who start cycles, they should not start on high dose and they should definately taper off and not quit cold turkey.