This is actually the method we consistently use with our daughter - with a few slight tweaks and it has worked well and doesn't feel "bad" at all.
When using any form of discipline (this is not synonymous with punishment) it is really important to set things up to be predictable. Predictability sets you up for success. A statement made out of frustration like, "okay you can have it for breakfast then." often doesn't work because it doesn't include consistency and predictability. It makes the consequence about your emotions rather than about the child's choices (and life lessons). These kinds of things often lead to the power struggle you describe in your question.
First of all we ask for eating in balance. We watched what our child ate and if she had fairly equal amounts of everything served we didn't worry about it any further (sometimes they really just aren't hungry). The AAP recommends that parents choose what foods are available, where food is eaten, and when meal times are, providing access to healthy foods at least every 2 to 4 hours. Children choose whether to eat, and how much.
Secondly, at our home, when we serve the first plate of food she only got about the number of bites of each item as years of life she has had - three years old meant three bites of everything, four meant four etc. Sometimes staring at a full plate can overwhelm kids and they don't even know where to begin. By giving small amounts like this, it is likely the child will eat what is on the plate and want seconds. We are not aiming for a "clean plate" kid here, but the rule that she had to finish most of what was on her plate before getting seconds was applied (we were flexible if there was only about a bite left of something). Then, she could get as many or as few seconds of her favorite parts of the meal as she desired. We knew she had sufficiently at least tried each of the foods presented.
Thirdly, we included the procedure for new foods too. If you don't, you lose consistency. However, we did not insist she try anything really spicy or rich in flavor as young children do better with milder tastes anyway (we simply didn't serve it to her - if she asked for some we gave her one bite to try - if she wanted more, we gave her more). Seeing the food at breakfast became a predictable outcome or consequence she actually would come to feel she had control over.
We don't threaten, cajole or discuss. She eats a "balanced" amount of food or she doesn't and we don't make a big deal about it at dinner. It may sound harsh not to give "warnings," but we generally avoid even this (minus one warning each night for the first week the method is used). The next morning we simply get out the "offending" left-over, place it in front of her and reiterate the importance of a "balanced diet." We restate the idea that since she didn't eat anything green the day before, she'll need to start her day with something green today.
The two most important keys are the consistency part and not getting emotional over it. If she eats the offending food - that is her choice; if she wants to wait and eat it as a left-over for breakfast, that is also her choice - she is the one that suffers the consequence (not me by being upset and worried over it).
Now, my daughter will even throw in extra bites of stuff she doesn't like when she knows we will be going to a party or something. At a wedding we recently attended, she approached me when it was time for cake and said, "Mom, I had 15 green beans, 5 bites of salad (obviously she is older now) a slice of roast beef and a roll. Will I still be balanced if I have some cake?" I laughed and said she could eat the slice of cake - I hadn't even intended on keeping track while at the wedding.
Now that she has things down pretty well, I can choose to be a lot more lax about it (like at events such as a wedding), but I did have to be a bit strict about things for the first little while to make she she really got the drill. I also adjusted for things like the late snacks you mentioned, or if she was ill or something and kept an eye out for possible allergic reactions to things. I really tried to make sure that first month I was as regular and routine about her eating schedule as was humanly possible in order to try to maintain that consistency I mentioned.