Routed access layer but still have default gateways live in the core?

Simple question. I would like to redesign my network so we’re using routed access layer (access layer switches have layer 3 routed ports up to the core/dist no vlans stretching/layer 2) but it’s super important that the hosts default gateway still exclusively live on the core layer.

For this we would not want to do any kind of tunneling like L2TP, and no other kinds of encapsulation like VXLAN etc.

We would also expect core redundancy to be seamless like if one core goes down the hosts will not drop any pings, etc.

I was thinking since there will be a layer 3 hop between the hosts and the default gateway that we could use proxy-arp to help the hosts get to the core default gateway.

To help the core get back to the hosts we could do souce-nat overload on the access switches (or should I say access ROUTER amiright) on the northbound interface.

The main advantage of this is the default gateway for the hosts is just a Loopback address on the core routers so you could have it the same on both cores and use anycast.

I labbed it up in GNS3 and ping is definitely working between two different access pods so I feel like the basic proof of concept is solid. What potential gotchas or issues could I run into?