Making an unrequested change at revision stage to a journal paper

Make the improvement

The review process is there to improve the paper. If there are things that you can do to improve the paper without the reviewers help that's great! Making the changes is helpful to everyone.

From the reviewer's point of view - there will always be comments from other reviewers which I didn't think of. I wouldn't expect all improvements to come from my comments.

From the editor's point of view - they way to publish high quality papers. The review process is one (very important) aspect of this.

From your point of view - you want your papers to be as good as possible.

I don't exactly disagree with @TomR, but - I'd say this depends on how deep the revision is, and how far along the process you are. If its fundamental enough, and the review process has been long and involved, then your new idea is essentially a different piece of research. In that situation, I would perhaps consult with the editors (or reviewers directly if relevant) about whether or not to introduce the change; or perhaps decide from the get-go that it's material for another paper, and mention the alternative method in a concluding remark, e.g. something like "The authors believe that XYZ can be improved upon using ABC."