Unrealistic aspects

Compared to modern theatrical productions, Othello seems to employ unrealistic conventions to me. The basic themes of the play are realistic, and common nonetheless. For example, jealousy is often used as a theme to a literary work, but displaying it the way that Shakespeare had is not so common. For example, Othello never questions Cassio about the suggested affair between him and Desdemona. If this had a been a realistic play, there would be some sort of confrontation between the two men. Also, instead of directly going to Desdemona to ask her about the affair, he avoids seeing her or bringing up the situation. It just seems odd to me that asking Desdemona and Cassio would not be Othello's first reaction to Iago's story. The relationship between Othello and Desdemona is also a tad unrealistic. If she is his most prized possession, then shouldn't Othello hold her word over everyone else's word? The way that Othello handles the news is unrealistic, also. His first instinct is to kill the both of them, but why not leave Desdemona? If it's because he loves her so much that he cannot deal with it, then YES it is romantic, but it just does not seem realistic. Only insane people kill out of anger or jealousy. Othello has no self control.