Is RC4 secure with a single-use 32-byte random key prefix and 3072 prefix bytes discarded? Are there any known attacks against RC4 if used with a single-use, random-generated 32-byte key, and 3072 random bytes prepended to the plaintext?

Are there any reasons why we should consider such a use of RC4 less secure than an other state-of-the-art stream cipher with a single-use, random-generated 32-byte key?
Yes, there are reasons to avoid RC4 and to consider it hopelessly insecure.

The single-byte biases—the biases that were so obvious that Bob Jenkins found them empirically on his 1994-era laptop within days of RC4's publication—may decay as you go down the keystream.  But these are the tip of the iceberg.  Many other detectable multi-byte biases have been identified that continue long into the keystream, notably in Fluhrer–McGrew 2000 and Fluhrer–Mantin–Shamir 2001, and applied in practice on TLS and WPA year after year after year.

The only reason academics chose to spend precious grant money on designing and implementing public attacks on RC4 is that people kept using it in important protocols against the advice of cryptographers for twenty years after it was broken.

That nobody has broken your protocol with RC4 probably just means your protocol isn't as important as TLS and WPA.

Just Say No to RC4, kids!