After going undrafted, he was still unsigned for four months even though teams knew they wouldn't even need to waste a roster spot on him his first year.
Davis had a bulging disk in his neck that was only discovered during his Combine medical exam. Such neck issues can be career-enders, even for players having the added value of NFL experience, much less a rookie.
The standard treatment for bulging neck disks is to do nothing but monitor the bulge and hope that it recedes on its own. Surgery is a last resort, and then only if the bulge is causing ongoing debilitating symptoms. At least, that's what my neurologist told me when I had mine. The thing is, if the bulge DOES shrink, it can take months to recede to the point where normal activities* may be resumed (* NFL-level football is NOT considered to be a "normal" activity in medical terms).
When the Pats signed Davis to a 3-year contract on August 11th, 2017, it was widely presumed, at first, that he was brought in as a Camp body to fill out the DE ranks after Wise suffered a concussion. However, it was later revealed that he hadn't been taken off NFI to participate in practice because he wasn't yet medically cleared for football. Whether or not he received medical clearance later in Camp is unknown, but the Pats may have calculated that there was no point in (irreversibly) activating him by that time.
Through last year, the rule regarding NFI players was that they counted against the 90-man off-season roster until final cuts - the earliest date on which such a player could be designated Reserve/NFI for the regular season. So, in addition to (inexperienced rookie) Davis not being medically cleared after four months (and still at least some uncertainty about his future health), there was a roster-spot cost for a team that signed him. So, it seems to me highly unlikely than many (if any) other teams were interested in signing him, regardless how good his pre-Combine tape and measurables looked.
BTW, this rule was changed for the 2018 season so that a player may now be placed on Reserve/NFI at any time and NOT count against the off-season roster (e.g., Darren Andrews).