Noiamnot - because we practice directed autonomous education, we constantly find ourselves testing and trying new things at the request of our DS. But family budgets, actual behavior track records and discussion about motivation for subjects always cuts short any whimsy.
What does that mean? DS began violin age at 3. Now, at age 5, he is not as "focused" as we believe he ought to be. Fortunately, the violin teacher "rewards" him with piano lessons when he can perform appropriately during his lessons.
In short - tuning in to your child is valuable. Explaining reality is a life lesson. I agree with Beetroot and Franniken - pick and choose where to spend your money. Exposure to a classical education is priceless. So, I invest in my wonderful, yet, deviant Suzuki teacher.
My DS gets drumming from the West African and Capoeira classes I haul him to. And as a person of African descent, I have to say I have always viewed "European classical music" with skepticism. There are so many ancient, relevant, cultural traditions to which we are just awakening. Balance is critical.
And learning balance is so important because we are living in a musical world informed by so much more than we learned as children. Some instruments are worthy of tuition - such as piano, violin, cello, and flute. Other instruments lend themselves to self directed learning - bass guitar, drum kits and harmonicas. The key is to research, evaluate, pick and choose what suits your family.
For us, there are lessons to which we will joyfully invest. For us - the five instruments associated with capoeira, West African drumming, (Euro)classical violin, and piano are worth our financial support. Many other instruments we believe can be self-taught or have familial resources upon which we can rely.
Essentially, you are the only one who can plot the advantages or disadvantages for your particular child. Only you can plan for the distinct educational outcomes you desire. Every family is different.
My only hope is that you will make a choice which best reflects your family's values and ability to support any self-directed learning your DC has identified.