But is he a luxury?
I don't expect the Saints to cut ties with Morstead this year as they carve out more than $10 million in salary-cap space. But the question must at least be pondered since Morstead is scheduled to make $3.5 million in salary and bonuses.
Morstead, 29, is also coming off of a down season by his lofty standards -- though that can easily be attributed to the quadriceps injury he suffered in Week 4 that forced him to miss two games. Morstead said he wasn't fully healthy until the final three games.
The Saints have never treated Morstead like an expendable luxury in the past, so there's no real reason to expect that to change now.
They appreciate the value of having someone so reliable in his position -- especially considering they've gone through a whopping 10 kickers over the past 10 years.
Morstead said the respect and loyalty are mutual.
"I think it's hard for players in the NFL, because there is so much movement. I think it's rare to feel a sense of loyalty to an organization, and I think it's rare to feel like coach to player relationship is not just that," Morstead said earlier this month. "Like (special teams coordinator Greg) McMahon, I love that guy. I'll be at his grandkids' wedding one day if I get the invite. To have had the amount of time with the same coach, the same head coach, the same GM and to feel the appreciation that they've had, it's been really nice. And I haven't taken that for granted at all.
"So it's just, in a lot of ways it was a frustrating year, individually and team-wise, but I definitely look forward to coming back."
The Saints drafted Morstead in the fifth round in 2009. At the end of that rookie season, he pulled off the surprise "Ambush" onside kick that helped lead New Orleans to victory in Super Bowl XLIV.
Then the Saints signed Morstead to a six-year contract extension in 2012 -- before he went on to make the Pro Bowl.
When asked about his future with the organization, Morstead said he's much more focused on the getting healthy part than he is about any potential release or pay cut talks.
"To be honest, I hadn't thought about it, really," Morstead said. "The only thing that was a bummer for me individually this year was just getting hurt. It was the first time where I haven't kicked off, and that was a big change for me. ...
"I finally felt healthy these last three games, and I think it showed. I think I finished out well. And I really appreciated the coaches and trainers, I didn't feel any added pressure from them to rush me back, even though I think they would have liked to have me kick off."
Morstead ranks among the NFL's all-time leaders with a career punting average of 46.8 yards and a net punting average of 41.1 yards (which ranked first all-time before the St. Louis Rams' Johnny Hekker moved past him this season).
Those numbers suffered a bit in 2015. Morstead's average of 45.6 yards per punt was his lowest since 2009. And his net average of 40.7 was his lowest since 2010. Morstead said he and the team decided to focus more on directional punting since he didn't think he could kick the ball as far or as high as normal.
Morstead does not believe it's the start of a permanent downward trend.
"Just talking to guys around the league, I know 30 is old for a lot of players, but for a punter it's pretty young. So I feel good," Morstead said. "I think for me personally, what's really tough is when you're out there, people kinda forget you're hurt, and you're not on the injury report anymore. So it's just dealing with that and handling that.
"But I felt like we handled it as best we could this year."