Just replying to give the question more visibility since I had the same question. I found this post online 13 where it says:

[…] Terminating the input in an end-of-sequence (EOS) token signals to the encoder that when it receives that input, the output needs to be the finalized embedding. […]

But this doesn’t make sense to me. Once the last word has been processed, the resulting hidden state is the last one. I cannot see any need to "signal the encoder to finalize the embedding (i.e., hidden state).
Have you compared the results with and without adding EOS at the input sequences?