If a rider finishes within the time limit, he is allowed to start the next stage.
Some of the riders who are lowest on GC are contenders for stage wins or are still factors in the points competition for the green jersey.
Tyler Farrar is currently in 176th, but he is an important part of the race. Mark Renshaw (Cav's leadout man) is in 161st. He is also a important for the race. Cav sits in 151st position, Pettachi in 152nd, and Hushovd in 137th.
These riders are not GC conteders, but are important for the race. There are many somewhat anonymous domestiques who fill the last 25% of the overall who are very important to their GC contenders.
The time limits weed out the sick and the weak. The only way to limit the field to the GC contenders and their best helpers is to eliminate the green jersey. That is simply not an option.