I'd disagree. The purchaser is an adult, but the customer is not. Who gets excited about a particular toy? That's the customer. (Note: I'm not talking about the edutainment market here)
Phrase it as you might. The adult is the one making the decisions. The children's excitement and desire is only one of the things the adult takes into consideration when buying a toy. That's a big deal for the parents, but much less so for the grandparents, uncles, aunts, etc. Obviously they want to make the kid happy, but they are distanced enough that they will probably not know what the kid actually considers the hot things. That's why when you were young you had many toys, but not always the ones you really wanted to have.
The adult isn't always the one making the decision. When I was a kid, I'd often be set free in the toy store and given some limit on how much I was allowed to spend. It was usually a low limit, but there was a good variety of toys under it.
The adult set the budget, but as the kid I had control over how that budget was spent, unless it was a toy my parents found objectionable.
Exactly, they had the final say. They were merely making their decision simpler. And that's the best experience you'd get. If you have family and friends, it's likely a good chunk of your toys were bought by them too. Toy makers have to appeal both to kids and adults.
For certain categories, the adult is definitely the customer. For toys aimed at children under three, the ads regularly talk about training hand-eye coordination and other basic skills.
For other categories, you could argue that the toy companies are selling a service: Make the kids stop complaining for a few hours. Naturally, an easy way to do this is to be the reason that the kids are complaining in the first place.
No, because the excited person does not get to make the decision. I do.
Also, good proportions of toys are not exciting to kids at all. Especially during Christmas and birthdays. They are swimming in sea of toys they will never actually play with, because it is simply not possible to play with that many toys.
This is an interesting distinction within any industry. Who's the customer? Ultimately what matters is how the buying decision is made -- who has agency.
Parents and grandparents are the ones who spend the money, sure. But the advertising is directed towards the kids.