As has been mentioned, 22 rim fire barrels are soft, with shallow grooves.
A jointed steel rod, like you will get from CT will wear the barrel out mighty fast.
We never used to clean a 22 barrel. Jack O'Connor once said what Mark pointed out, cleaning them wears them out faster than does shooting them.
I bought a used Winchester Model 69A in the mid 1960s. I may have cleaned it when I got it, I can't remember. But recently, I began reading on CGN about people cleaning their 22s and about lead accumulating in the barrel.
My old 69 had been shot a lot in competitions and regulated shooting, plus a lot of years of general shooting, since 1965. So, I decided maybe I should clean it, the first time in over 45 years!
One wipe through it with a cloth and it was a shiny silver.
However, in very recent years, I acquired a 22 that had so much lead in the barrel that I could hardly see though it.
So what is the cause of them occassionally leading the barrel now?
I don't think it is the ammunition. I tend to lean toward microscopically rough barrels from the factory, on occassion.
In any case, if I bought a new 22 I would shoot it for a while, then clean it. If it wiped clean with no sign of lead, I would not clean it until it had shot quite a lot, and if it was still clean, no more cleaning.
My opinion.