You need to download the entire Blockchain, if you can't download it, you wont be able to index and verify the transactions and form your own UXTO set.

The purpose of the whole process is to ensure that every transaction is valid and the client is able to build their own UXTO database. It doesn't make sense for a client that can't do these basic stuff to exist. If you just want to only create and send transaction, you just need the UXTO.
Great... There goes our trustless and decentralisation nature. If you're only going to send the UXTO set, your client will not be able to see the transactions that was made (at least till a certain date). I don't really see a point in making a client that doesn't show the old transactions. How am I going to track my spendings? Blockexplorers?
So in the future, if someone DOES actually spend the dust outputs, how does the client handle it? It doesn't recognize it from the UXTO set that it has. Its quite bad if you were to query another node when you receive a transaction with an output that you don't have stored locally. Additionally, how do you ensure that the full node that you make the request from doesn't lie to you? How are you going to verify if what they tell you is true?
The real advantage of Bitcoin Core is mostly the fact that its trustless. If you're going to destroy it, might as well as just use an SPV client. Sure, they may be less secure than Bitcoin Core in a sense that they are susceptible to sybil attack, the client that you are going to develop will essentially be worse.