If challenged, I could do this on demand with an amount of the challenger's choosing, to 'prove' I have control of the funds.
Yes, it is possible to send to the same address. However, to prove control of an address, you could instead sign a message.
Transactions come from an account (wallet) to an address contained in another account. If you have 2 btc in your wallet, they will actually be made up of a history attached to each fraction of those coins ever spent in a previous transactions. In other words you have fractions of coins that add up to 2 btc.
When you spend/send btc in a transaction your account bundles the fractions to equal the new sum. If the fractions don't add up equally to the new transaction total, you will receive change back to your account, most likely in a new address created during the transaction.
If the goal is to consolidate multiple addresses in your wallet to one, it would be prohibitively difficult due to the these fractions of btc. I would create a new account with one address then send your entire balance there.
This is not needed to prove ownership.
Please correct me if I'm wrong.