I think simply stepping on the spray painted circle would be enough to break it. At least temporarily. Which could be pretty powerful if used right
Bender does this when he is calling his minions. He's got a wire circle he can fold up and pocket, but it unfolds in a split second, and he uses it to pump out his gray men like one per second, each time breaking the circle by stepping on the wire.
You can create a circle with virtually anything, provided it has the capability to represent a line in the sand type barrier. By that, I mean that it should be somewhat visible, tangible or anything along those lines, so you can distinguish "in here" from "out there". Sand, salt, glitter, sawdust, paint, people standing in a circle, a USB extension cable, an actual line in the sand/dirt, gravel, light funneled through prisms, flowers planted in a pattern, and so on. It depends on what your circle needs to do. Do you need to use a lot of energy, in which case it should be a more durable material, or is it just supposed to be quick and dirty?
Chalk is just one of those things that's often used for a reason. It's cheap, easy to carry, quick to use, etc. And it is gone with the next rain. If there's always going to be a paint circle on the ground where something has happened, people are going to get suspicious.
Anything that makes a circle, even an imperfect circle can be used
Including just a mental image of a circle, as Harry uses in Changes
If you read through a lot of the books, circles that are being used just for basic circle properties (such as blocking out things made of ectoplasm, separating the magic of the area inside from the magic of the outside for Thaumaturgical working, and acting as a cage for supernatural beings from summoning) can be used no matter what the circle is made of.
The issue starts cropping up because of three things. One is practicality. Circles that are made by nothing but some scratches in the ground is really easy to disrupt by just environmental problems. Harry mentions in one of the books that it would be incredibly dangerous if debris came by and brushed away the circle in the middle of a working. The second has to do with making circles more powerful on their own. When circles are made from certain materials they function better in certain circumstances. Certain objects and materials in the Dresdenverse are shown to have power independent of belief (Iron hurts the Fae with or without belief, White Vampires can't deal with objects touched by True Emotion etc). When these objects are worked into circles the circles function better against those things either protecting what's inside or trapping the beings inside.
The third is something that Harry only hints at a couple times, but it has to do with the way that the circles seem to work. (This is almost complete speculation but considering the way that the magic of the Dresdenverse seems to work more as a fundamental force like gravity and light some of this might make sense.) They function by taking the initial investment of energy and constantly running that energy on the ring of the circle. To overcome the circle, a being must be able to overcome that energy and destroy the "wiring" of the circle as it were. The energy of circles seems to function by inhibiting any supernatural or magical force from passing through its bounds. Mortals are able to break it because their free will is not impeded by the energy, but supernatural beings have no free will so they can't break the energy around the wiring. This is also why random environmental debris can mess with the circles as long as it isn't "empowered" by a supernatural force or will. At one point Harry mentions that having a circle be perfectly round helps to make it more efficient, so it also begs the question if certain materials just conduct magic better like there are certain materials that conduct electricity and kinetic force better. One big thing that comes up for me is the use of objects when Harry attempts to trap a strong being. This is about creating and using images and concepts in his own mind to reinforce the spell. However there is a specific instance in Cold Days where Molly uses magic to try to overcome a Sidhe spell and are able to do so through the use of iron. This has nothing to do with belief and more to do with iron's relationship to the Fae.
Of course this is all speculation and I'm somewhat rambling, but it's an interesting thing to ponder.