The purpose of a kitchen countertop overhang (usually about 1-1/2 inches) is to prevent spills from dribbling down the face of your cabinets, and to keep crumbs from dropping into the drawers and cabinets below. If you think your cabinetry will stand up to liquids dripping on them repeatedly over time, and you want to deal with crumbs inside drawers (you think it won't happen, but it def will), then forego the countertop overhang. The absence of the counter overhang is also considered a contemporary look.

I wonder if those pictures are of a butler's pantry or a serving sideboard in another part of the kitchen. A counter with no overhang doesn't seem practical for an active part of the kitchen where messes need to be cleaned up. Your cabinets would probably suffer the consequences.

What is the set up of the cabinets under your countertop area? Are they all drawers with handles? If they are like this pic, could you do the bottom two drawers with handles the way you like them and just do the top drawers with knobs?

Another downside with the handles installed in the rails is that their attachment screws do not go through the drawer box front also, allowing the drawer front to possibley work it self loose.

I think it may depend on how wide your rails will be. Mine are ~2 1/4" wide. I have my handles set into the top rail, and have no issue with enough room to grasp - but I don't have big hands, and I notice that I tend to go for the top drawer's pull with an underhand approach -- which has plenty of room.

My handle screws do go through the drawer box, but my installer had to be careful to position the handles in the right spot (not too high) to do so....1/4" higher would had been too close to the box edge.

I have mine there and it's not an issue. I also have a counter overhang.

However my drawerfronts have a little bit of a frame above them - unlike the photo where there is ZERO frame

I am also debating how much of an overhang to have in new house, as I like the look of a flush counter. I pretty rarely spill things on the counter - so I don't expect liquids to be repeatedly dripping on them

Wow! Thanks everyone! It's rare that I get such great advice :) I had completely forgotten about the overhang preventing spills and crumbs so that is completely out. I think I'll have to stick with the handles on the panels instead. I love the idea of using knobs instead so I'll play around with that a little. :)

Just keep in mind that handles do spread the stress on the attachment point out, as opposed to knobs which concentrate the force of pulling on a single point - a consideration for a drawer as opposed to a door.

I'm just not a fan of the look in general.

My kitchen guy is telling me that it will be too hard to grab the handle of the top drawer because it's too close to the counter top.

I kinda agree with your kitchen guy in theory, but you can easily test it. Buy a cheap handle and tape it (securely tape it) to your current drawers. Try opening the drawers and see if you find it problematic. Obviously you'll need to be gentle in your opening/closing, but it'll be enough for you to form an informed opinion.

Is it a bad idea to have no overhang?

Yes, it's a bad idea. It means your handles will protrude beyond the drawers, and that means you may knock into the handles as you walk by -- it'll also look kinda odd. I also agree with the above posters that dripping things down the front of the cabinets will be a (small) problem.

I'm just not a fan of the look in general.

Agree.

It may not be the look you want, but cup pulls might work since you'd be reaching to the underside of the pull.

^
That is so smart!!!
And there are so many cup pull styles.

https://www.houzz.com/products/channing-cup-pull-3-3-4-c-c-flat-black-prvw-vr~159177594

I also agree to have some overhang of your kitchen countertops to prevent spills and drips on your cabinets. I personally think centering the hardware on your drawers in the panel and not rail, gives a more balanced look.

My DMIL has the pulls on the panel. On the top drawer, the panel is so narrow that it is hard to get your fingers between the rail and the pull. On the bottom drawer, it’s a reach. For the middle drawer, it’s fine.

In her case, pulls on the rail would be better. She’s 94 so easier is better. But I think that easier is better at any age.

You could place the top pull in the center of the panel in the top drawer and the bottom pulls slightly higher in the panel on the lower drawers, so that those bottom pulls are slightly easier to reach. It's not the same look as you wanted, but it is slightly more functional than having the lower pulls placed in the center of the panel. Or you could get a cabinet with wider rails to carry out your original concept.

I’m a pretty tidy cook and I’m always amazed how crumbs find their way in the drawers and drips on the front of my cabinets. Perhaps the rest of my family isn’t as tidy 🤔