The money could be spent more wisely.
Aside from spending less on a comparable WR, the Bears could spend the other half of the franchise tag money, and fill a hole elsewhere. That surplus could be spent luring in other attractive free agents the Bears so desperately need.
What holes do the Bears need to fill?
Quarterback

It goes without saying that QB is an issue. Whether the Bears decide to ride the Hoyer/Barkley express or not remains to be seen, but there are far too many options to remain static at the position.
Offensive Tackle
According to Pro Football Focus, the Bears had the 15th ranked offensive line, but “Chicago’s interior was arguably the league’s best.” That means the offensive tackle combination of Charles Leno Jr. and Bobby Massie is probably worse than most realize, and definitely ready for an upgrade.
Defensive End
The majority of expert mock draft compilations have the Bears taking Jonathan Allen
. In some cases Solomon Thomas or Derek Barnett are even thrown into the mix at #3. Clearly there is a need at 3-4DE.
Secondary
There is obviously a need in the secondary. At CB, Tracy Porter is the best option, but has frequent nagging injuries. Kyle Fuller is inconsistent, and on the verge of first round bust status. At safety, nearly every Chicago Bear fan alive has daydreams about Eric Berry; so, it’s clear that safety is a need.
If letting Jeffery go means the Bears pick up DeSean Jackson and Stephon Gilmore, or Terrell Pryor and Tony Jefferson, it’s an obvious choice.