Durability for a dining table, that I understand, but looking “natural” is very subjective. Ok, we won’t bury the top under a 1/2 inch of epoxy, that’s not natural, but where to draw the line? Do you consider shellac natural? It’s a film finish, so not a “close to the wood” finish, and shellac certainly “enhances” and can easily “darken” wood to which it is applied.
Anyways, for the last handful of decades, a pre-catalyzed lacquer, sprayed from a gun, has been the best answer for durability and quality of results while still minimizing time to completion (which means it keeps costs down). New coats melt into the previous coats, so repairs can also be made perfectly.
However, it is a film finish, like shellac and so you might not find it “natural”. Like shellac, you can minimize the darkening by carefully selecting a version specifically designed to avoid darkening, but most believe it doesn’t “enhance” grain and chatoyance as much as shellac, so perhaps you’d consider a pre-cat lacquer to be more “natural” than shellac.
It might be the king of durability, at least among the common dining table finishes, but it will require a spray gun, probably a spray booth, too, and proper protective gear for yourself — both for application and any repairs.
Recently, hard wax oils like Rubio and Osmo have become much more popular. They are “close to the wood” finishes — the exact opposite of a film finish like shellac or pre-cat lacquer. They were invented as floor finishes, so they are durable, but in a very different way from the pre-cat lacquer I mentioned above. A pre-cat lacquer will form a barrier protecting the wood beneath. Slam your keys into the table, and the wood underneath is undamaged, even though the finish itself might show a big set of scratches, delaminations, dents, and certainly will require a repair. You could say it tends to maximize the appearance of damage to the finish.
Hard wax oils are the opposite — slam your keys, and the wood will take whatever damage it takes, but except for the area where the keys actually removed finish, the finish will be undamaged. So it tends to minimize the appearance of damage to the finish.
They don’t require any gear to apply, especially if you get a 0 VOC version — wipe them on — but like high-end lacquers, they tend to be expensive. They are very easily repairable — just scuff or sand the damaged area, and re-apply. Unless there’s been changes due to UV, the repair is going to be invisible, and if you get the 0 VOC versions, you can repair the piece in place. Also, they all seem to offer a version which has a minimal darkening effect on the wood.
Given your criteria, I think this is the direction you would prefer, relying on the strength of the white oak to provide the durability. You’ll be doing regular cleanings and repairs with children, but that’s always the case.
In between, you can get a not-so-bad dining table finish by combining shellac undercoats topped with a wipe-on poly for durability. However, it probably won’t be natural enough for you, if I understand your criteria.
It’s an age-old question; good luck and post pictures when you’re finished!