Hi Kevin, the wild parts of my property would be 100% wild rose within a few years if we let them get away with it. I leave a few patches because they are a great pollinator attractant, smell good, taste good, and are pretty.
But, yes, they spread through rhizomes along with through birds eating and pooping the seed.
I use a 'garden weasel' to soften up the earth above the roots and then pull what I can out by hand. My record is a 6 foot long root!
Constant pulling of the young plants as they pop up will eventually cause orphaned root pieces to run out of energy and die off, but it takes a few seasons.
If you want to put in the effort, you could cordon off sections with a buried barrier like roofing metal or plywood.
They like it a little bit acidic so you could weaken them by sweetening the soil around their bases. Also, pick every single bloom and make rose syrup, jelly, bitters, infused salts, or just eat them in salad or as garnish.