Interesting idea. I would suggest it as a play style where all LS's are placed in LoBs at the beginning of the game, and the following cards are not allowed:
Son of God
Burial
Falling Away
Hopper LS
Lost Souls (2 or 3-line)
Any card that shuffles LS's into decks
Hormah
And the following rule could be implemented: All heroes have access to all sites. Thus sites can be used for other strategic purposes (Kir, Lion's Den, Site Discard LS's, etc.) but not for lockout.
That way, it prevents winning games by LS management/Sitelock. Other deck building rules could be added, but I will leave that to others.
I think it could be interesting.