Why is it important to have a restriction point? (G1-S phase control)
The reason you want a check point in the transition from the G1 phase of mitosis to the S phase of mitosis, is that the cell needs to make sure that it synthesized all of the necessary proteins, and accumulated the necessary compounds with which to have DNA synthesis begin AND complete. 

The transition from G1 to S is a point of commitment for the cell. There is no turning back at that point. It either needs to faithfully replicate the entire genome or it should die. An incompletely replicated genome would be disastrous for the cell.

If it tried to arrest and go backwards it would likely have too many copies of certain genes and those gene products would likely cause lethality to the cell. You would end up with all sorts of errors and breaks where replication forks collapsed. It would basically be death for the cell. What would be even worse would be if this cell was actually able to avoid the death signals, and at some point enter the cell cycle with all of these damaged chromosomes and you are looking at the possibilities of cancer.

If it arrested and then proceed to G2 and M and somehow got through those checkpoints, then you will have two daughter cells with incomplete genomes. Again if they could survive at all, then likely end up becoming good candidates to proceed down the road to cancer.

That is why G1 needs to be completed properly before the cell commits to replication. It is a point of no return and needs to be tightly regulated for the benefit of the multicellular organism.