Algae scrubbers without sump

Hello all. I’m doing my very first build and have asked a lot of questions on here and getting my tank set up and I appreciate all the help. It’s a 55gal long tank. I’ve decided not to do a sump with this tank. Mainly because my wife is worried about a leak in the living room. Talked to a few people on here about skimmers, refugium and algae scrubbers. All in all I’m leaning towards an algae scrubber. Trying to keep everything self contained as possible so my wife doesn’t freak out lol. After she see it up and running I’m thinking 100+ gal tank and the 55 gal long as my sump but that’s later.

So my question is the actual algae scrubber growing algae to clean the water or to give the algae somewhere to grow and that alone cleans the water. I’m thinking it’s somewhere to grow as I can’t see the algae cleaning anything but I’m new to all of this. Or it could be both.... I was thinking a Santa Monica hob5 system or depending on the way it works building a self contained sealed system that uses a return pump to pull water in and back to the tank. Any idea on that will be helpful.

Thanks in advance
Matt