AFAICT, DLO is not an NEC recognized flexible cord type nor a Chapter 3 wiring method. Yes, there is DLO that's also marked at RHH/RHW-2, but to the NEC, it's RHH/RHW-2. (I much rather people use type W if they need fine-strand/flexible and are under 600 volts.)
I have lots of experience in non-NEC environments (mining, marine) where we aren’t encumbered by ULs NIMBY policies.
DLO will be almost always dual rated RHW-2 or RW90 even though it vastly exceeds both ratings. Type R is a catch-all for generally any cable with a rubberized jacket. The jacket is CPE which is the same material used in mining trailing cables where it gets drug across the ground, rocks, etc., all day long. It was originally developed to connect a locomotive generator to the motor which is a high vibration and oily nasty environment hence the name. It’s also designed for maximum flexibility which is an advantage with tight radiates on many poorly designed DC systems from a bending radius point of view. It is this flexibility and toughness that makes it vastly preferred over W.
Type W eschews the tinning. It uses EPDM as the insulation/jacket which is significantly less flexible and less abrasion resistant with about the same thickness. It is considered light duty in the mining business. The flat version is used as submersible pump cable. A lot of it doesn’t bend much at all and is a pain to work with. It gets stiffer over time.
The ultimate jacket for toughness is TPU. It is stiffer than either of these and a royal pain to terminate it but if you are worried about tearing it up, this is it. It is an option for the hard rock miners and I’ve seen it occasionally in SO type cords but it is horrible to work with for the most part. So you will see it sold as some other cable type but with the TPU jacket.
That’s from a purely engineering point of view. But there is a major hassle with DLO. NEC has never recognized it as a type of flexible cord even though it obviously is. Even in its original use it’s intended as permanent wiring inside a wire way , not a “super cord” beyond SO ratings. Most of it is rated “for CT use” but not exposed run rated. Type RW90 and RHW-2 are designations for permanent wiring. So this is very annoying but you have to run it in some kind of wire way. A cable tray is fine but it has to be continuous. At the ends of the tray it needs a piece of flex or something to run inside unless you design the tray for continuous support and protection. That’s not the way I’d say 95% of the installations are actually done but that’s what Code calls for. Obvious running across the ground is sort of like having an infinitely wide tray with a solid bottom so that would be the correct derating factor. It’s not free air.
Even if you switch to W, portable cord rules still say no running through doorways, over rough edges, etc. as an example a particular generator installation I know of had 87 relaying but it was a very big loop. The 87 CTs were installed at the generator bushings (12,470) at one end and at the substation breaker 2500 feet away on the other side of the step up transformer, much like a power plant GSU. The 87 relays were set to trip if current differential exceeded 600 A! It kept tripping and they spent millions sending the generator (over 50 MW) off site to test on a test stand. Transformer and all wiring received obscenely expensive tests. Nothing found. All but swapped out all 87 relays and these were old monster induction disk relays that require someone in good shape just to remove them. Turns out the CT wiring didn’t have any grounding or plastic bushings. Over a period of about 30-40 years of vibration from the generator it finally cut through the jackets and intermittently grounded the CT. The permanent fix was to determinate, pull a little excess cable, slip on and screw in a plastic bushing, and land wiring again. Maybe a 15 minute job. I can’t remember how many times I’ve seen DLO and others destroyed costing tons of downtime because of poor installation practices.