The shrubs growing on the slope look that they have been there quite a while and seem to be growing straight up. (Sometimes, if there is a bend like an old-fashioned walking stick handle in the stem near to the ground, that bend can indicate that the land is slumping.) About the tree roots showing: there's not a great deal of topsoil from what I could see so the roots have probably spread out to forage for food and water. A number of tree species have suface roots - some quite gnarled and obvious. Think swamp cypress for a start. Unless the trees are very tall and your local prevailing winds are fierce or unpredictable you aren't likely to get windthrow. On a slope such as yours I'd be looking for grooves cut by runoff from the top as the precursor to shallow gullying - and that didn't seem to be happening. Personally, I wouldn't spend on 'posh plants' for such a slope. I'd ask for 'pioneer-type' shrubs - preferably native to your area. If you have a native plants nursery near you - pick their brains. Grasses, creepers, low-nutrient environment shrubs and sub-shrubs. That soil is obviously not rich - it hasn't been colonised by much at all. If you need clues and there are cuttings at the sides of your roads check there for what will establish and thrive and stay seemly. (No one needs a slope covered in fire risk weeds!) When you visit with the plant place/s ask for SPECIFIC guidance on how to plant up a steep slope. If it has a high clay content - let them know because it will change what they will advise. If there is any better soil available on your lot, and you can spare some - mix it in with the slope soil when planting but don't bother putting in fine compost. All that happens is the plants grow out to the limits of the top grade environment and then either sulk or die. Think about buying your reveg plants in 'root trainer' tubes rather than big cans or baggies. They'll be younger and better equipped to strike out, rootwise. Hear you when you say you're budget-constrained. See if you can legally collect native seedlings of suitable plants, grow them on, then plant out. Sometimes a neighbour can be a good source. Under the bird feeder, in a garden, can be another - but expect a lot of berry-producing plants ;-) And, as the slope is a bit of a challenge - could you devise a ladder to get you upslope for planting? Or a scaffoldiong arrangement. Something with wide enough treads so you don't end up with anguished feet!

There are so many options..... California natives are a natural choice. The Las Pilitas website has a ton of good information to get you started. Look up Ceonothus, Rhamnus (now called Frangula), Ribes, Rhus as a starting point for shrubs for along the fence line. its always good to mix in some deciduous plants. I really like Holodiscus and Physocarpus which have seasonal changes.. I'm sure others can suggest more. But don't feel the need to be a purist and choose only natives, Many Mediterranean and South African plants are from a similar climate and there are many wonderful choices. Grasses soften everything as they move with the slightest breeze. Again, there are tons of choices. Google can be your best friend in checking out possibilities.

I think if you paint you’re setting yourself up for maintenance. Embrace them - you’re in Arizona & they‘re everywhere! Once you add things to look at, you’ll stop seeing the wall. Looks like rock on ground all around fence so maybe inground planting not an easy option. You could invest in huge & decorative pots, place strategically & fill them with permanent type colorful plantings. It‘d be good if you’re able to install some kind of drip system to provide summer water - even one you hook up to a hose that waters all at once & on timer for low maintenance. Maybe also keep your eye out for wall art to hang which would add another dimension of color & design.

It looks like a fence and the neighbor has a hedge. Who has the arborvitae? But yes, you can stick a bush in it. You will have to move the pots, the rhubarb, the green hosta and give up some lawn to do it. Now a close city location is needed for appropriate plant suggestions. Your snow picture says the right selection of Yew might be what you need.