Liches don’t have to use phylacteries, they can, but they often proven to be… meh.
You have to put a part of your soul into the object, and with how this world works, that means a part of your power. Plus that means leaving behind, somehwhere, a part of you that can be destroyed or channelled into spells against you. And with the number of adventurers snooping around, you can randomly lose parts of your soul and power forever.
Those objects can actually be tracked, all it takes is a mage that can recognize your aura and then they can search for it and destroy it.
It’s similar to how the romans did it. Gladiators are entertainers first and foremost, like pro wrestlers, the goal is to put on a believable play for the people, give them a show they’ll remember. Death is actually extremely rare. Except for war prisonners (Meidia does that, mostly), which are put to the death in the arenas by different scenarios, all for the public’s enjoyment.