Alright, well getting arrested and caught sucks as you have a record, and your prints and DNA are on file for life.

But, in my idea, Chris Criminal can turn this to his advantage.

Chris Criminal drastically changes appearence. He goes quite far from his hometown, and he gets some reliable local details (place he can use as adress, etc). Fake ID would seal the deal, but probably not neccesary.

He needs to get himself arrested.

Yes, you heard right. A minor crime that will just be a caution, perhaps shoplifting.

So, he gives fake details. Walks free. If his prints ever come up in a investigation, police focus on his non existent alter ego.

Could this work, or is it just a unattainable daydream?

There's always the risk of them finding out you aren't really who you say you are if you do this, especially if you get yourself arrested. It could work, though, at least until they realize the person you were when they arrested you isn't real or has been dead since before either of the crimes (depending on your method of getting a fake ID).

If your prints come up in an investigation without you doing this before, though, they don't have anyone to focus on... but they still aren't focusing on you (provided you haven't been arrested before), so I'd say it's a lot of work for not very much more chance of getting caught. Not worth it to me, but you could try it and tell us how it goes. :P

this^

Trust me, if you get arrested they'll figure out your id is a fake. If you don't have an id, they'll make sure they know who just the fuck you are.

This is pretty much just using an alias? Many people do similar to what you've said and nearly always eventually end up getting caught.