Using the PCB itself as a zero insertion force socket?

In my honest evaluation of your proposed idea it is nearly impractical. You should be strongly thinking about a 8-pin DIP Clip that you attach to your programmer board with short flexible cable (think silicone insulated wires).

DIP Clips can be found in many places but this picture from the AliExpress web site does a great job of showing how to simply insert your bare IC into the clip.

Picture Source: https://www.aliexpress.us/item/3256809349438841.html

Some ideas that come to mind:

• Two rows of plated thru-holes on 0.1" pitch, spaced apart somewhat more or less than the standard 0.3" (possibly two rows straddling 0.3"?) to force the DIP pins against the walls. I'd be a bit concerned about wear.
• Single-position receptacles for square pins, but sized for larger pins than the DIP actually has. Some testing may be necessary to find a size that gives consistent connection with minimal retention force.

First off, the "easy" thing you might not have considered: a DIP-8 also fits in a DIP-10, -14, -16, ... zif socket.

The other thing: yes, what you describe can work, but badly without very controlled alignment and uniform prssure and aligning contacts by hand is terrible and prolly lot more work than using yoir DIP-8 socket with a good IC lifting "pincer" tool.

I'd instead go for 3D printing a recepticle with 8 conical holes into which the 8 legs of the DIP IC can "fall", with spring loaded contacts underneath to make reliable contact once a slight force from above is exerted. The springs mean you dont have to exert very uniform force.

This idea can work if, and only if, you currently have an error-free programming experience. A quick look around this site for folks having issues like "failed to program", "invalid chip ID", "target not found", "no power to target", "programmer not found", sums up the experience of most hobbyist programming activity. If you have the programming issues nailed down and never have trouble like this, then you are OK to try your idea. Because if there's a problem, you know that you just need to press harder or realign the chip. But if you combine this with any of the other issues, you will go insane trying to find what is causing the problem this time. I know, because I have tried stunts like this.

If this is a production environment, the immediate answer is no! To that end, and for better reliability, the DIP clip as described by @Michael Karas works very well, and in fact we had a similar situation and found you can get the same thing in SOIC format--so your board could be even smaller. There is also a product called "Tag-Connect", which is a connector with 6 (or more) pogo pins that make contact with pads on your board, a lot like your original idea. The cost for your board is only the area for the pads and alignment holes. Here is a photo I took from a sample board they provide.

I've done something similar before to make a socket for a custom module, but that used heavy spring pressure to press contacts reliably against gold-plated brass contact blocks soldered to the PCB. (This is quite similar to how DIP ZIF sockets work internally, actually.) You may be able to do something similar with two PCBs or a PCB and a 3d-printed part, using one to apply sideways pressure to the leads relative to the other. Gold plating is a requirement for something like this, as you get no wiping action on the contacts at all. You can use one pressure board on either side of the contact board to brace the leads against bending stress.

I wouldn't bother, though, for something as simple as a DIP-8. Just use a ZIF socket designed for a higher-pin-count DIP, which are readily available.

If you don't need true zero insertion force, you could also get a low-insertion-force socket; not all sockets require the same amount of force to insert a part. Mill-max, for instance (no affiliation, I've just used their parts a lot), specifies insertion force for all of their contacts (see pages 250-262 of their catalog); in particular, their #35 and #43 contacts are the right size to accept DIP pins and have very low insertion force of around double-digit grams per pin. Here are a couple single-pin receptacles using those contacts, though you may want to look around at other options, as these are just some of the first search results I got: #35 contact and #43 contact.