Here is a past thread that may help:

Eliminate countertop overhang?

"Jennifer Svensson

4 years ago

We also wanted zero overhang for the look but were advised to go with a minimal one. We ended up with 1/4” overhang which still looks good in our opinion even though it was a compromise. We have drips on the cabs but we had that with the 1.5” overhang in the previous kitchen too- no difference there for us."

Here is a link that has a pic of that kitchen but the overhang is hard to see:

HELP! Kitchen backsplash time: Jennifer Svensson

Inset is not modern. It is traditional. Combining the two is beyond weird looking and destructive to the cabinets.

Please lose water drip worries. That's silly.

Not silly at all. Water drips ruin cabinets.

I looked at photos from an architect that designs very modern residences. It's kitchens have zero-overhang countertops.

What makes cabinets look even sleeker are recessed handles like these IKEA VOXTORP Drawer fronts. Note that the countertops in the photo are not zero-overhang; the countertop extends 3/4" over the 7/8" thick drawer fronts.

If the overhang is only 6/8" and the drawer fronts stick out 7/8", then I cringe at the crumbs, etc., that will gather in the recessed handles. They will need to be wiped out daily in work areas and, over time, the finish can be damaged with constant wiping down (although it probably won't be noticeable unless someone is using the drawer).

Contrary to what some others say, water drips will damage cabinet finishes. I've seen it many times at friends' houses and in my old Kitchen in my previous house. The biggest issue, of course, is sink cabinet bases. (Our new house has an apron sink and I'm worried about the cabinet doors beneath the sink.)

Inset cabinets usually have a 1/2" to 1" overhang. I also agree that inset is a very traditional look. Frameless is modern look and can be very sleek looking.

Buehl: "If the overhang is only 6/8" and the drawer fronts stick out 7/8", then I cringe at the crumbs, etc., that will gather in the recessed handles."

The countertop is 25-5/8" deep on a 24"-deep cabinet. The countertop extends beyond the drawer front: 24 + 7/8 + 6/8 = 25-5/8.