OK, so after a lot of screwing around I figured out what's going on here and how to deal with it. These instructions are for iOS 13.2.3.
Prerequisites:
1) You have to be willing to make a contact card for yourself in your own contacts list. Yes this is painfully stupid but there doesn't appear to be a way around it.
2) You have to have location services on and have internet access when you try this (it won't work in airplane mode or a basement with no signal).
3) You need to pick a numbered street address that Apple/Maps can find in their own database.
The procedure is as follows:
1) When you open Maps, tap on the home/work icons. Maps will prompt you to either set up a new contact card for yourself or link to an existing one, pick the 'create new' option.
2) In "your" contact card, you can skip the name and other fields, but you have to create a new 'home' street address field. Within that field, you MUST TYPE OUT a full street address and it has to be something Apple approves of because the phone has to phone-home this info to Apple HQ. You can't picky a dummy address. You can't pick a valid address that Apple doesn't like. You can't just open the Maps app and place a marker next to your pulsing blue dot and set it as 'home'. You MUST type in the whole complete Apple-approved address into the contact card with the keyboard: no other method works. If you try to do this offline or with a bad address or a map marker, it won't "take" and Maps will kick you out and act like you never even tried.
3) After you've filled that out, create another field and set this one as 'work'. Enter the exact same address info as what's in the 'home' field.
4) After you have both the 'home' and 'work' fields filled with Apple-approved address info, then and only then will the Maps app register them as legit and give you the blue "i" icon. If you filled out both 'home' and 'work' with the same address, Maps will glitch out and the icons will rapidly blink in and out of existence and shuffle around a few times before the 'work' entry disappears and only 'home' remains.
5) Now you can tap the "i" and then tap "remove favorite" at the bottom. However even after you've done this it's not fully gone it just gets removed from the quick bar in the main drawer. If you tap the "see all" link in the drawer, 'home' will always show up at the bottom of the list as a "siri suggestion".
6) Having done all this, you can't delete the dummy contact card you created for yourself. Doing so will reset Maps and make both the 'home' and 'work' icons come back and you'll have to start all over.
This whole process is dumber than hell but it appears to be the workaround. As usual, Apple expects you to set up your life exactly the way the hipsters in California do and if you try to deviate from that narrow path you're left jumping through a hundred hoops.
