Lot's of people play that way. I played that same scheme. The problem is our players haven't bought into it or don't want to because it's more work for them.
If you are shooting gaps then it actually can become easier to block you.
I've never heard of defensive tackles needing to read and react.
It's pretty simple. You either beat the guy blocking you or he beats you.
When you're so close to the LOS, you should be disrupting play design, not waiting for the play to develop to decide what to do.
This is the same exact problem with the Hurricanes defense.
To augment and finalize my point, let's look at how Suh performed when he was a penetrator/disruptor in Detroit versus now where he is being asked to read and react.