I use a Park Tool every once is a while. At first it was messy, now I can keep the rest of my bike and my hands fairly clean. I use Simple Green. Cleans chain up fine, perhaps not perfect (but what I can see or hear I don't care

). I rinse off chain with hose and drive water in between links.

But I also rag dry well and bang out chain and ride a bit to dry it off. Sometimes put some squirts of WD-40 to help drive out water. That along with 115 deg at 4% humidity typical summer evening gets the water out quickly, even if deep. Then I dry/wipe down good again to get any bits of WD-40 (if I used it) out. Then apply a lube (ATB) spin it up, rub in with fingers and let it sit overnight before wiping it clean.
It may not be perfect, but it gets most of the grit out, keep chain shiny, smooth, rust free and frankly I expect to put a new $15 chain on at least once a year or so if I push it anyway just like one puts on new tires once in a while.
Al