It depends on your location about how trendy it is, or whether it might even be on the way out. In the Chicago area it has become so widespread we are seeing it in housing developments and new condo buildings. That can be a sign it is no longer special, since it has "reached the masses" haha - therefore people who are into watching that kind of thing will not be putting waterfall island counters into their kitchens. The last charity Design Home I saw (they take a mansion and have different interior designers do each room, then have tours, and the proceeds go to charity), the kitchen island counter was super-thick wood (maybe oak), heavily polyurethaned for a high shine, with an old-timey slightly distressed stain so it looked like reclaimed wood, but wasn't. It must have cost a ton, but I'd say that will be the thing to do for $150k+ kitchens, and the waterfall stone counter won't be. But that is super high end, FWIW.

I am a fabricator. A plywood underlayment for 2CM is typically complemented by a 4CM drop edge which masks the underlayment on the edge. the plywood is really just a spacer as it does not contribute significantly to the structural integrity of the overhang. For 3CM quartz a "fussy" fab shop will grind the underside of the overhang to remove the printed Logo's from the OEM. If requested the fabricator can polish the underside but the fab shop polish will not be of the same quality as the surface. However, it will be good enough to look finished on the underside. Polishing the underside is NOT an option typically offered by the fabricator. In my business we've learned to ask the question when the layout of the room, and particularly the stairway location, means the underside will be readily visible on a regular basis and not just when someone is on the floor looking up. Another option is to make the overhang "double thick" where 2 pieces of the engineered stone are mated back to back so a factory finish is on both sides. This is an easy option for 4CM assuming corbels are used or the double thickness is extended back over the cabinet. Finally, some natural stones that are crack prone have a fiberglass matting epoxied on to the back of the stone to help it hold together during transport, fabrication, and install. A competent fab shop will remove this backing as a matter of course. I am always annoyed at the poor quality evidenced by a job where the backing can be felt and seen on an island overhang and even on the narrow countertop overhangs. If you really want a great looking underside the best way is to double up the material back to back. It's an expensive way to do it for a variety of reasons.

Damiarain - thank you - food for thought - we were wondering if we could fit a little table in front of the bench looking into kitchen - the window looks out into common walkway so not much of a view. I also wanted to thank you for recommending we swap oven/micro - which we did and it gives us more landing space to left of cooktop - I realized I must not have saved the most recent modification to thinkdesignlive's drawing - here is the top picture again with shallow pantry, and entry table noted

@Beth H.  The current gray tile is actually pink stone tile that we couldn't identify but had it diamond ground *because it's so hard), steamed cleaned then painted and sealed.  I like the uneven look and the cool feeling of the stone under my feet that you can't get from porcelain or ceramic.  Initially, we were going to replace it but it sits on 2 inches of floated cement and nothing is really level in this house and chose not to go that route hence if we replace it would need to go on top of the current floor and/or repaint. The carpet is inset but if we were to replace the floor then we would fill it in.