Not a bad idea, I had to open TD account for my daughter me being custodian until she turns 18. She saved up some cash and wanted to learn investing.
your kid would appreciate it because daddy gave his daughter a head start (a chance to retire early (as you know the early 1000s of dollars would earn more than the 1000s of dollars invested later).
on a side note, some people just have a wrong idea about money management. They just load up on student loans, then ask for forgiving (I think that's just wrong: somebody gains, someone else losses). They should have a class in high school's curriculum "money doesn't grow on trees".