Why does the sec allow brokers to not only buy and sell for us,  but also for themselves?:
The official reason is that they make an 'orderly market'. They must buy and sell to keep the market from sudden and dramatic shifts. So they are forced to buy and sell under certain conditions. 

It is also true that the make full use of opportunities to buy and sell when they can make money. 

It's an unpleasant trade-off. 

I don't agree with them or with this policy but that's what is happening.