Lightning is still evolving and you have to make some choices about how you want to use it. To get a static address you need to have web server providing your LNURL to an active node. Otherwise your payments require the wallet to be open and synced to generate an invoice. This is where centralized services come into play.

inb4 someone says “BOLT12 solves this!” which might eventually be true, but it isn’t widely available yet.