It wouldn't be the first time it happened. The Pats tagged Cassel and everyone knew they had no intention to sign him long term. Most player who have been tagged and traded, everyone knew that the team tagging them had no intention of signing them to a long term deal for whatever reason (they are a valuable player they don't need, the two sides are worlds apart on a deal, etc.). That is why most tag and trade deals happen immediately after the start of the new contract year.
Now the Pats are up against the cap and would have do several moves just to franchise Jackson. And then, they would have no money to make free agent moves without freeing up a lot more money. Other teams could use that against the Pats in any negotiations. The longer Jackson would be on the cap during free agency, the more hamstrung the Pats would be.
I am guessing if they had the cap space they had last year, they would have made the risk of tagging Jackson. But with them only having about $7 million of free cap space and needing over $17 million of cap space just to tag Jackson, that played a big role in their decision. If they couldn't trade Jackson in the first few weeks of free agency, it would stop them from making any moves.
The cap space issue is one thing I didn't factor into the situation. Teams know the Pats couldn't afford to keep Jackson on the roster for the first weeks or month or so of free agency.