As for an oral route to the intestines, enteric-coated microspheres has been used to support delivery of pancreatin. But IIRC, there was some controversy concerning the reliability of this route for widespread applications; some of the problems being variable release rates or low penetration of intestinal wall or too rapid degradation upon arrival.
I know that bromelain, a proteolytic enzyme, has been used as a debriding agent in burn therapy. Using that as a keyword, I found this
link which indicates bromelain
may be an active sinus and nasal anti-inflammatory. After a few other spot checks, IMO, there seems to be a body of positive evidence but which tends to be of the lower quality case-study and expert opinion type; although there may be a better quality cohort study or two. Current standards for evidence-based medicine are typically higher.
Like TS&M mentioned above, my impression is that there's an economic factor at play here. High quality studies are expensive and I suspect that there's not much perceived return on investment for what could be an unpatentable herbal extract treatment for a relatively "unglamorous" condition (stuffy head) for which there already are treatments.
*A general discussion and bits of history about enzymatic meds is given
here
**There seems to be increasing interest with the role of related MMP's (matrix metalloproteinase) with inflammation and mucoid production as related to asthma and COPD as mentioned in this
article.