Making best of bad situation
The Lakers could cut Kobe and erase his contract from the books (although they would still have to pay him the $30.4 million remaining on his contract after this season). Not only would they save tens of millions of dollars in tax payments, but they also would again have the ability to improve their roster via the full midlevel exception, the biannual exception and sign-and-trade deals. They wouldn't have Bryant, but he likely will spend most of the season rehabbing anyway.
There is a catch, but even that would work out in the Lakers' favor, if they want to take advantage of it. When a team uses the amnesty clause on a player, it cannot reacquire that player until the expiration date of the contract. For example, the Houston Rockets let Luis Scola go in 2012 with three years remaining on his deal; as such, they are prohibited from reacquiring Scola until 2015 (when his original deal would have expired).
In Bryant's case, his contract would expire just about the time he's ready to return to full health. Therefore, the Lakers would be able to bring him back just at the time he would be worth bringing back, presumably. (We're assuming that he can make it all the way back, but it's not a given, based on the history of NBA Achilles tendon injuries.) And if he can't get healthy, the Lakers wouldn't have to sign him.
The hit would be too big
Remember when Kobe Bryant was standing in front of his locker, leaning on his crutches, moments after rupturing his Achilles tendon? Remember when he was asked whether this was his last game and how incredulously he looked at the reporter? That was my reaction when I heard this question.
To quote Bryant that night, "Really? Really?!"
Yes, Bryant suffered a serious injury that will sideline him six to nine months. There is a chance he could miss the 2013-14 season; there is a chance he might not be the same player again. Then again, there's also a chance he'll be back by the start of training camp and pick up right where he left off on opening night.
Even if there's a 50-50 chance of either happening, the Lakers cannot risk the massive hit they would take by releasing Bryant to save roughly $80 million this summer. Bryant is a big reason the Lakers are one of the most popular teams in the world and were able to ink a $5 billion TV deal. One of the perks of signing such a deal is removing even the thought of releasing the most accomplished player in team history to save money.
I believe Bryant will be back before the start of this season. Other players have returned within six months after suffering the same injury, and no athlete on the planet has the will and determination of Bryant when it comes to overcoming injuries and proving doubters wrong. Bryant doesn't want to leave Los Angeles or the Staples Center. The Lakers know that if they cut Bryant, he could simply walk down the hall and sign with the Clippers and help them win a championship with Chris Paul. The Lakers know they can't let that happen for financial reasons or basketball reasons.