Process running in SSH-allocated TTY not terminating once stdin is consumed

Question

I can perform file-transfer via SSH^* like this:

ssh -T ${HOST} eval "cat > remote.txt" < local.txt

However, if I instead allocate a TTY, it hangs until I press Ctrl+C:

ssh -tt ${HOST} eval "cat > remote.txt" < local.txt

Question: Why is this? Is there a workaround?

The best I can figure out is that the local EOF is not being propagated to the remote process.

_{Platform details: OpenSSH_5.3p1, CentOS 6.7 x86_64}

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_{* In my real use-case, I want to use this approach to transfer files directly to a remote sudo user; I can't use SCP because I can't SSH as the sudo user. The sudoers file in my target environment has requiretty set, hence the need for a TTY.}