Some of the support parties have tried that, and have been shut out, so the government reaches across the aisle on certain laws. Our previous government tend to do the budget with the opposition party rather than their support party, for these reasons. And the same with our current government.

The only problem is that if the government cannot find an agreement across the aisle, they have to go to their fringe support party. So the opposition always have to wager this when negotiating. If they don't want to find an agreement with the government, the result might be worse than a compromise. So it is an advantage to the government in negotiating positions sometimes.