None of the roads leading to the major parts of the parks require an SUV. My recollection of Zion and Bryce is that all the roads are paved. You must want to do serious off-roading to find dirt roads in Canyonlands and the major sights of Arches are accessible on paved roads to their parking lot; some walking may be required.

https://flic.kr/p/vmZUpD

I did drive a few dirt roads in Utah with a rental car when we went to see Arches, Canyonlands, Goblin Valley and Capitol Reef. Unless there has been rain within the past week making things muddy, you should be fine with a car. If it is muddy, please turn around and go back to pavement.
The two dirt roads I remember were out to Crystal Geyser SE of Green River and to Copper Ridge (east of 161 about 21 miles N of Moab). I completed Earthcaches at both locations after a walk of less than half a mile. At Copper Ridge I took photos of dinosaur tracks in surface rock.

I live in Utah and road trip to all of the parks and surrounding roads--dirt, etc. You will be fine in a sedan unless you want to go off roading--e.g. you need a jeep--or you want to go on some roads on Cedar Mesa or to the end of Hole in the Rock Road outside of Escalante. Otherwise, the roads are just fine in a sedan,

Most if not all rental agencies prohibit taking their cars on unpaved roads (doing so would void the insurance) -- so it doesn't matter all that much whether you rent 4wd or not.

Thank you for the info everyone
EK

For Moab, you can rent a jeep for the day to go on some trails, ranging the gamut from oh-hell-no to just off-the-beaten-track. You only need a guide for the most extreme. DH and I have twice done this and driven the Shafer Trail and some other similar. We've used Canyonlands Jeep Rentals and one other, can't recall the name. You pick up in the morning and return that afternoon, after hosing off the worst of the dirt. You can pick up a map and decide which might be for you. Shafer Trail might be a bit too adventurous, from your first post, but it's still tame enough for us (we are definitely not thrillseekers).

The Copper Ridge Dinosaur Tracks (GCZD9A) are 2.1 miles out a dirt road east of US 191 north of Moab. It had not rained recently so I had no problem driving out at about 15-20 MPH. The trip out to the Crystal Geyser was about 6.5 miles of dirt road SE of Green River (town) along the Green River (GC1BPNY). Over 200 geocachers have visited these sites over the past 11-15 years. Many of then have driven cars instead of 4WD or high clearance vehicles.