SPOILER ALERT:

Because it's about a principle. Not about the depth of his feelings for her. Ilsa died to save her, and Ethan is honouring her sacrifice.

Also, I disagree with you about Ilsa's demise. I think it is built up to well, deftly telegraphed (I predicted it the moment she said about never having been to Venice), and carries dramatic weight with a good send-off. It's sad because she's been such a great element of the previous films, but I think narratively it was satisfying.