I use a stainless steel immersion chiller, but instead of running cold tap water through, I feed it from a bucket of ice water and a sump pump. Basically, I do the pre chiller setup you mentioned not wanting, haha.
I figured I may need a sump pump at some point in my life, so I got one for about $35 and the chiller itself was cheap too. The entire setup was cheaper than a plate chiller and works great for me. I basically run cold tap through until the water leaving the chiller isnt super hot, then I put the outlet hose of my chiller back into the ice water bucket. Once I do that, I can basically leave it alone. So, I let the cold water recirc while I just sit back and drink a beer.
I bet plate chillers are an overall faster process, but this was cheap, uses less water, and I can sort of set it and forget it. Works like a champ