I would definitely follow your dentist
's advice. I certainly do see your point about wondering why filling
baby teeth would be important, given that they will eventually fall out anyway.
However, the main issue is that if there is a significant cavity, this could potentially lead to a more serious tooth infection. Tooth infections in children are important and should not be ignored for several reasons.
First, any pain that your child feels from the tooth could affect their ability to eat. This could have serious implications for their nutrition and for healthy growth and development.
Secondly, a serious tooth infection in the a baby tooth can pass all the way through the tooth and affect the forming bud of the adult tooth that lies just under the baby tooth. Therefore, an untreated infected baby tooth could actually have negative consequences for the permanent adult teeth.
Finally, an unchecked tooth infection could lead to a more serious body-wide infection, for example if the bacteria in the tooth infection get into the blood stream of your child.
Talk to your dentist about your concerns, and I am sure they will be happy to explain why they think filling the tooth is important.