Hidden buy order above Best Bid is jumping the lit queue, right? So before Best Bid is taken out, your order will fill (let's assume all major exchanges are at Best Bid). Obviously, if best bid moves, you need to adjust. Basically, the lit quote is something you can use to make decisions knowing it is protected and will be routed to.
So the hidden orders are very likely to fill prior to the NBBO getting taken out. I agree but that's not the same thing as "prior to other lit orders".
Exactly ... part of "smart" routing.
I think you are thinking of HFTs as some parasitic arb seeking conglomerate, but SOR is part of HFT and may be used to provide client with best execution depending on what they need. There are no "best" way to find liquidity, it depends what it is you are trying to accomplish.
Keep in mind that every instrument is different, so what works for liquid stocks may not work for mid-cap or low float. There are no one size fits all solutions.
Correct me if I'm wrong, I don't think most smart routers will sweep for hidden liquidity. With IB's SOR you can do it by ticking the "seek price improvement" checkbox, but it's disabled by default because it slows down execution.
In general it's not really clear to me if there's any advantage to placing hidden orders inside NBBO (compared to lit orders) unless you can do it on multiple exchanges at once to reduce the probability of tradethrough. Then you tradeoff under/overfill risk with the benefit gained (less HFT gaming, etc).