Is it a good idea to protest for a paper rejection? Say that you submitted a journal paper and after some time you received a rejection. The comments of the reviewers were not that bad. Some of them are demanding minor revisions, some are demanding major revisions. The Editor however rejected the paper saying that the proposed model is unrealistic.

Is it a good idea to send an email and protest for such decision?
Before you protest, you should decide what, if anything, you want to accomplish. If you improve the paper and resubmit it your protest won't have counted for much, and you need to improve it anyway because of the reviewer comments. But the editor has questioned the underlying model, so this may be the wrong venue for publishing this work. 

I suggest you think about the editors comments, improve the paper with the reviewer comments in mind and either resubmit or submit elsewhere. The last option may be best.