A home that brings an enormous amount of utility to Anarchist blessed decks, House of Many Faiths does a lot with its ability.
First, the ability to shuffle a card in your discard pile and hand into the deck is deceptively powerful. Not only does it let you clear things you don't want out of your hand, it can also effectively increase the frequency of any specific card in your deck. Being able to keep cards like Unprepared or job actions like Kidnappin' in your deck can help to adjust your plan for specific matchups, allowing you to run a few less of specific cards while still seeing them frequently.
I've found a lot of luck cycling in specific miracles I need to draw like Amazing Grace, or combining this ability with The Joker's Smile to keep jokers in your deck at all times and create a powerful draw engine.
HoMF doesn't quite provide the generalized mobility of the base 108 home, but being able to unboot a blessed and move them to town square, with +1 influence to boot, is nothing to scoff at. Unbooting allows the possibility of mollifying the boot cost of such miracles as Soothe or Confession or allows for running jobs like Epidemic Laboratory without taking one of your key dudes out of the action permanently. It often feels like having an extra dude available at all times, and can be key to controlling the position of dudes in town.
The downsides to the home are mostly that it doesn't do anything for you until you have a miracle on the board, so it makes sense to run enough miracles to get one in your opening hand pretty consistently. The "Move to town square" line of the ability can also be a mixed blessing. It's a powerful position for movement purposes, but can make using the home ability very dangerous against decks that aggressively control town square. Of course there's always Amazing Grace which can help stop your dude from being called out immediately upon hitting town square.
Overall the home is definitely worth it, and I personally would be hard-pressed not to use it in basically any anarchist deck with enough miracles. 5/5