There is no point trying to obfuscate addresses by sending redundant data, that would just massively increase server load for honest SPV servers while doing little to nothing for the malicious SPV servers. You absolutely can push your transactions to a random node, assuming you're not actively having a targeted sybil attack on you. There was a wallet that actually did exactly this, but I forgot what wallet it was (only vaguely remember looking through the code for that).

The problem is that bloom filter or whatever methods being used by most wallets uses are fundamentally flawed. The onus should be on the wallet to change their ways of querying the server in a bid to improve privacy. Wasabi for example, uses BIP158 which requests for the entire block as well as additional decoys from their peers. This would be far more effective at tackling the root of the issue.