About 3 years ago I started making a concerted effort to completely overhaul my diet and eat healthier. One step was to eat less fast food. I haven't completely eliminated fast food, but when I do indulge, I no longer order French fries due to their high glycemic index and high calorie count. For me, no French fries means no ketchup sachets.
At home I still eat ketchup (e.g. with sweet potato fries), but I've completely switched to homemade lactofermented ketchup. No cooking is involved if your base starting point is canned tomato paste. Making a two-quart batch of homemade ketchup takes only about 30 minutes of prep time and yields a supply that lasts for months. (About the equivalent of 300 ketchup sachets.) After mixing the ingredients and transferring to a few mason jars, you leave it out at room temperature to ferment for 2 or 3 days before going into the fridge.
Many believe that lactofermented vegetables like kimchi, cold-fermented sauerkraut and traditionally prepared ketchup are very healthy. As a collateral benefit, there is very little waste. The tomato paste cans can be recycled. One also uses whey poured off from plain yoghurt as a starter culture for the lactofermentation, and yoghurt containers can be recycled.
I use the ketchup recipe from Sally Fallon's Nourishing Traditions cookbook, more or less, though I add Coleman's mustard and sometimes use honey instead of maple syrup. I always follow the recipe proportions exactly for sea salt and nuoc mam, since salt content is important for inhibiting undesirable bacteria.
My ketchup story is just an example. I think that one will generally find that efforts toward healthier eating and getting away from highly processed foods will have the desirable side effect of non-recycled waste reduction.