There are some exceptions. Cutler had said before his contract that he would have no problem with it. Greg Hardy actually said he would love to get the franchise tag. In Cutler's case, he may have just been saying the right things, but in Hardy's guess, I bet he means every word of it. A guy who has made less than $3M his entire CAREER suddenly gets a guaranteed $12M for just one season and gets to stay where he's comfortable and then get another shot at a long-term deal?
That's the problem with the franchise tag really, it's not one size fits all. Guys like Brees and Rodgers would be ridiculously underpaid at the franchise tag amount relative to their market values. Same will apply for Graham if he actually does get a TE tender with the tag. A guy like Shields, as much as I like him, would be pretty overpaid if he signed a franchise tag. Even though he might not like it.
Look at Charles Woodson. Signed the franchise tag 2 straight years for the Raiders in 2004 and 2005. He made about $20M for those 2 years, for $10M a year (probably about $12-$13M a year now adjusted for inflation.)
Then he finally got a long-term deal which was worth $7M a year. Some guys make out pretty well on the tag. It's usually an overpay, it just puts the player at risk without a long-term contract. But I can tell you if I had a guaranteed $12M in front of me to sign for one year, that would be enough to set me and my family for life.