There are some HUGE benefits to setting up an allowance. Doing so, and giving your kids control of their money, is very empowering and engenders positive associations about money. In a society in which so much negativity is directed towards money and the accumulation of money (some warranted, some not), wouldn't it be nice to raise of generation of kids who used money for what it is - a tool. Nothing more. Nothing less. No baggage.
Giving an allowance can also help you reduce the "I want 'ems." You know, you go to the store with your child. "I want this. I want that." Making them responsible for small purchases can dramatically reduce in-store tension. Remember, I'm not saying the "I want 'ems" will end, but you will certainly have a context for a conversation rather than a knock-down, drag-out war in the store.
And don't forget that an important part of the allowance formula is to set savings goals. Teaching your child to set and achieve goals is arguably one of the most important life skills you can teach them.
Is the time burden of a weekly allowance stopping you? Do it bi-weekly or monthly. Whatever you do, make it purposeful and take advantage of its benefits. Good luck!