Privacy from Government investigation into our finances is already something we dont have. Not unless your a proponent of Tax Evasion.
We all have to declare how we earn our money, in order to pay our taxes. Even Prostitutes have to declare their earnings. Using a Tumbler service is not going to change the fact you need to declare the source of your income. Unless of course it's coming from an illegal source or you're trying to avoid paying taxes on it, in which case the Tumbler service might help you out, but again thats not a legitimate legal use case.