Nobody is going to stop you from feeding baby food to a baby or young toddler. Any child that is too young to eat the few solid foods on the kids' menu (which are largely junk anyway in many places!) needs to have baby food or a bottle. A good restaurant manager would much rather have 2 adult diners and a non-purchasing child than no adult diners at all. Moreover, no restaurant is going to want to press the issue with a child with food sensitivities, so older kids can get away with this too. I don't think you should be forced to feed your child just crackers because there's nothing on the menu for a 3 year old. That's not a meal.
If a child has serious food allergies that have not been addressed, and which could be triggered by cross contamination in a restaurant, then you keep taking your own products. When my 8th grade students took a field trip to Washington DC and NYC, we had one student who had diabetes and celiac disease. She could not eat in any restaurants. So she took all her own food and utensils and there was no problem with it. In some cases the restaurant was called ahead of time, and I think there was a physician's note with the chaperones or in her wallet. Believe me, no restaurant wanted a serious reaction from one customer and they were happy to comply. If a wait staff person was unclear, a chat with the manager would suffice.
That said, if you continue to go out with an older child and pack your own food, the child never experiences the tastes and the fun of dining out. The child never learns to try new tastes and textures. The same problem happens if they just expect to eat soup crackers or the little jelly packets - they develop bad eating habits. So it's not something you want to encourage long term. I'd stick to healthy choices like the cut up grapes rather than the cheetos. But certainly when a child is still on soft/pureed foods, you take your own food and your own baby spoon if you want. You can try to order something for yourself that your child can taste even if it's a couple of pieces of pasta or a tiny bite of meatball or a piece of a broccoli floret. You can also ask for a small side dish of something they have as a garnish - grapes might be one thing, or a few cubes of melon or a banana at a breakfast place, etc. They'll usually throw that in for free or charge you a very small fee such as $1 which you should willingly pay.