I am sure your managers told you this and they probably believe it but chain restaurants tend to have a lot of hacks on their management staff.
The thing is that the restaurant business is a hospitality business and the more hospitable you are to your customers wants the more customers you will have. Regular customers are what keep restaurants in business. Lucy can't find anyone to sell her food off of the kids menu. If you do it she might come to your restaurant every week. Let's say she comes in every week and spends $7 on a kid's pasta and a coke, she usually brings a friend and they spend the average amount a customer spends in your restaurant, we'll say $15. That is $1144 per year. 20% of the time she comes in you are on a wait so you lose $8 ten times a year or $80 per year. That is a net gain of $1064 per year from serving one adult food from the kid's menu and getting a new regular as a result. If you didn't serve her what she wanted that would be an empty table most nights.
I am the head chef of one of the busiest restaurants in Minneapolis. Part of how we got to be that is we have a reputation for being the Nordstroms of everyday restaurants in the sense that we try to accomodate every exasperating pain-in-the-ass special request our customers make. Obviously we draw the line at things that are physically impossible but in general if you want to buy something from us we try to sell it to you. Let's say this tactic gets you 100 new regular customers a year, using the math above that is a bit over $100,000 of revenue growth per year. We do more than double that but you get the idea.