From my experience I find running to be a good way to to make the work outs more versatile. (The same goes for weights) After doing so many boxing training it is hard to do some more. But you can still run then and that way you can work on stamina and burn fat.
so you like running for variety? best burning fat results comes from lowering calories and interval training, can do that with boxing drills which i find more specific to the end goal of becoming a better fighter.
To me it is not a black and white thing. I like it for both variety, stamina, and burning fat. Of course you can lower calories. But I rather train the fat off than go on a diet.
'Using weights' is a very general term. If your coach is saying stick to 25 - 30 reps, all you are really going to gain is muscular endurance. If you want to gain muscular endurance, then great, go ahead and do 25 - 30 reps. To be a complete fighter though, you need to focus on more aspects than muscular endurance. You need max strength, explosive strength, muscular endurance, conditioning etc, and this is in addition to the obvious skill work. To lay it out simply for you, try to assess what it is that you need to improve on... say max strength for example, and build your programme around this aspect. If this were the case, you could use the rippetoe programme (or similair), and on the non training days, throw some full body HIIT into the equation. If you find that you have plenty of strength, but you lack the conditioning to apply it for more than a couple of rounds (think Shannon Briggs), then you can limit the max strength to 1 day per week to maintain this aspect, and focus the rest of your training on conditioning and muscular endurance. We can all lay out this programme or that programme, but to maximize any programme, you really need to match it to your current abilities and tailor it to your goals.