I'm a licensed real estate agent, I actually got my license not just to learn about the business but to be able to save myself on agent commissions if I want to make an offer (if you can pass a CS data structures class you should be able to get a real estate license online in a matter of months), and I still would not try to optimize on closing costs.
Do I shop loans ? Absolutely. Are closing costs a scam ? Absolutely.
Would I try to optimize closing costs in the context of making a purchase ?
No.
In the time you have to decide the one really important question (whether to proceed or not) you need to spent it understanding the worst possible parts of the transaction you are about to make, NOT focusing on the closing costs.
Some class action lawyers should be worrying about optimizing these fees. Shop your loan, but spend your time investigating the property.
Pretending to be a site helping mortgage borrowers not get scammed while actually being a mortgage lead gen portal though : chef's kiss.