Look at SOPA/PIPA. They simultaneously pushed the same bill through both chambers to try and guarantee it would pass. Grassroots efforts led to it being overwhelmingly blocked in both cases. And then they just slowly slipped most of it's provisions through other legislation over the years.
I think we should be at least several decades past looking at the USA as a particularly functional democratic system...
The US constitution, despite its biblical status in their culture, manages to be more of a distracting throw-word ("LOOK at how this bill helping provide healthcare OBSTRUCTS your CONSTITUTIONAL RIGHT to NOT CARE ABOUT THE POOR!" (Ok, not a great example)) than a functional constitution that limits institutional overreach.
Your opinion is fine and all, but it's moot to this point.
The exact same things are happening in the EU, as evident by this very legislation this thread is concerning.
Except for a few types of bills that customarily originate in the house, most bills are introduced roughly simultaneously in both houses so that the information for debating the bill doesn't have to be brought twice. This obviously doesn't guarantee a bill will pass because it is required to pass both houses.
Every bill has to go through both chambers, but they usually originate in one and then are passed to the other once the originating chamber affirms them.
It is not common to push two independent bills simultaneously, despite your assertion so.