There are a lot of benefits to getting your children involved in your budgeting discussions. I don't think they should have a say in what you spend money on, but they should know (depending on their ages) that it takes a lot of money and hard work to pay for all of the basic needs for a family. They will then start to take some ownership of their contribution, they'll see the importance of conservation of some resources (like shutting off the lights when they aren't in the room, taking shorter showers, unplugging things they aren't using, etc) and not just a rule you made up!
I also think it's good to have the kids work with you on setting some goals for getting out of debt or saving for a family vacation. If they know what the goals are they will be less likely to "fight" you on your 'no' to certain things they've been used to having. They may even find ways to chip in financially if they are old enough to help with that.
One of the ways that I think this could be the most useful is for setting goals about cutting back on eating out or family activities that cost more then you want to spend. If you have a family meeting and decide what is a reasonable about of money and times/month you can do those outings the kids will see the bigger picture. That is also a great time to then share with them that it will require work from everyone to make it happen. Lets just use eating out as an example, if you are used to eating out 4 times a week and you've decided to cut it back to once a week, then you can explain to your kids that everyone will need to chip in at dinner time, so it doesn't all fall on you to make this goal happen. Also point out that everyone will benefit from the sacrifices you'll be making, by enjoying a family vacation or freedom from bills, etc.
These conversations are further preparation for them and their future financial decisions. Most parents don't want their children to struggle the way they've had to. What better why to prepare them then to teach them how to be responsible and make decisions that will help them have financial freedom (not everything they want).