I think the whole "processed" vs "unprocessed" food label is too imprecise to say anything about whether it's healthy or not. I don't think there's anything that implies that processed foods have to be unhealthy. It's just that most processed food tend to be less healthy.
People like variety.
Also, people may still like eating meat, but want to eat less of it - not for health reasons, but for the environment and to kill less animals.
"fresh" sausages most likely contains some of those preservatives too, as they prevent worse things like botulism. Unless maybe they're made the same day as you consume them?
According to our local, nitrate free, butcher freshly slaughtered meat contains enoigh natural nitrate-alternatives to not require additional nitrate if ham, sausages and so on are prepared soon enough.
nitrate-free is a myth. They use celery powder which breaks down to sodium nitrate. The FDA allows the producers to call this "nitrate free" since they are not using sodium nitrate directly and the FDA considers the celery powder a flavoring agent.
Chemically it breaks down to sodium nitrate and has the same carcinogenic nitrates. Its just a legal labeling loop hole.
Making a sausage is a form of processing. Sausage is a processed food, no matter what. The distinction is whether or not it is highly processed (i.e., amount of additives).
When the processed food tastes as good and as fresh as the one you cook in your house - why not. In the case of European plant-based meat, this is the case.