Can an open loop system replace a close loop system
Too long for a comment.
Think about the physics of the problem. Due to small variations in the components of the  plant, the original system may change from \$\frac{1}{s+1}\$ to, say, \$\frac{1}{s+1.2}\$. Then your scheme of cancelling unwanted dynamics won't work.
The situation becomes much much worse when the original system is an unstable system. The original system will get damaged due to its instability while the output of the cascade system hides that fact.
More over, even if the parameters don't change, very very very rarely do we know the exact transfer function of the original system. So this scheme is not suitable for practical applications.
To see why closed loop control is necessary go through the first few chapters of any basic control system text book. They will give more reasons for utilising closed loop control.