Anyone ever go with saw cut concrete that looks similar to this? It seems like a better way, compared to stamping, to get a simple, modern pattern such as large squares onto concrete. Anything I should be worried about doing this?

Yes

Also yes.

A) Yes, as in you've done it, it's great, and would do it again

Or

B) You've done it, it didn't work well, and I should be worried about something?

I'm assuming this is green (freshly poured) Concrete?
I guess it's possible you're planning to pour a stamped overlay topping on existing Concrete.
Make sure you're mix aggregate and blades provide least chance of spalling.
Also need to decide on width and depth to provide aesthetic you're looking for without trapping as much debris as possible or seal the Sawcuts with darker caulk to give the contrast appearance.

This will be green concrete, and there's an existing portion I would like to overlay to match. On the latter though, I'm concerned the overlay might have issues with this method since overlay I'd think would have to be pretty thick to work out?

Depending on size of existing section I'd say your best bet aesthetically is to demo and repour for continuity. Even if you get the stamping to match the sawcut you'll still need to attempt a color match which is trickier than it sounds

Can't demo existing as it's a large covered patio that's simply brushed concrete at the moment.

Sorry, yes I've done it on our patio. No issues other than the lines collect dirt that I have to wash out occasionally. Not a big deal though.

1. Was surprised one year when a top builder told our clients that tile would be a better/cheaper finish than stamping/staining their foundation slab concrete surface .. so also get tile bids.

2. Of course do not cut deep enough to a) cut the reinforcing steel nor b) expose this steel to rust ... either galvanized steel or 3' concrete cover, etc.

3. Explore the other other options that can present such a look from design/builders that offer all the options so you are not oversold on just the one option one may offer

4. The main complaint INside a house has been that a dining room chair's leg gets stuck in a concrete surface chip all the time.

If needed, and if the covered patio portion isn't post tension reinforced, you could chip down/roughen ~1-1.5" off existing to add sufficient thickness for new overlay pour and use small aggregate size for this section to match color and Sawcut aesthetic.
Granted this is starting to get a bit complicated. All things considered I would probably look to stamp the entire project as this will likely be more straight forward and offers a larger variety of patterns for end user preference.

If you opt to Sawcut I personally would seal the grooves with the darker self leveling caulk. You can likely do this part yourself and save money rather than paying someone to do it.

Also, factor in sun intensity/duration or shade cover as Concrete will transmit/radiate the heat so may make it difficult for bare feet. The original image also looks like it would be high slip risk when wet. Might be worth looking into your stamp options with Kooldeck or similar more heat tolerant product.

Not super worried about it getting hot. Lot's of shade and afternoon sun falls behind house so.

Not a fan of the look of Kooldeck products either.

Appreciate the replies. Will have figured out soon.

Have you looked into laying pavers on top of the concrete?

https://www.artisticpavers.com/

Thought about it, but adds cost.

Taking with contractor this morning so will see where things land.

Light acid wash, shallow decorative cuts, and a penetrating sealer. Clean look/ easy to maintain