My ISP seems to use just normal DHCP for assigning addresses and honors re-use requests. The only times my IP addresses have changed has been I've changed the MAC or UUID that connects. I've been off-line for a week, come back, and been given the same address. Both IPv4 and v6.
If one really wants their home systems to be publicly accessible, it's easy enough to get a cheap vanity domain and point it at whatever address. rDNS won't work, which would probably interfere with email, but most services don't really need it. It's a bit more complicated to detect when your IP changes and script a DNS update, but certainly do-able, if (like OP) one is hell bent on avoiding any off-site hardware.
I like the die-grinder microphone. Sets the tone for the rest of the presentation.