It's too big of a risk.
As I said, van Persie is unquestionably a great player. He was the Premier League's top goal scorer last year, and he's one of a few players that teams have to plan around.
Yet for such a strong player, van Persie is surrounded with too many question marks.
The first problem is that van Persie is very injury-prone. He's only started in over 20 Premier League matches in two of the last seven years. When he can stay on the field he's a huge asset to his team, but it's been difficult for him to do that.
Van Persie always seems to be out with some kind of nagging injury. Soccer (or football, depending on where you live) players take a beating every day, and some players' bodies simply aren't up to the task. Over the past few seasons, van Persie has proven to be one of those players.
While risking van Persie getting injured wouldn't be a problem for Arsenal under normal circumstances, it's a major gamble considering how unhappy he is.
There's also the matter of team chemistry to think of. I know that chemistry is played up to the point of being almost clichéd, but it's still tremendously important.
A professional soccer team (or really any professional sports team) cannot win a title unless they either get along or have such overwhelming talent that it just doesn't matter. Arsenal doesn't have the latter. That means that they need the former.
Van Persie has already publicly called out management for the direction in which the team is going. This guy is supposed to be the captain. He's supposed to be the leader and the one that everyone on the club instinctively trusts. Do you really expect that trust to still be there?
I mean, when a guy makes it clear that he doesn't want to be around, why on earth would his teammates want to play with him? I can't think of a reason.
That's a problem because soccer, more than almost any other sport, demands teamwork. You need to know where your teammates are, you need to know what they'll do and you need to be able to respond to that accordingly. When it comes down to it, I don't think van Persie and his teammates will be able to play that way anymore. Not the way that they used to.
Arsenal should wrap up the van Persie saga as quickly as possible and then try to move on with new signings Olivier Giroud, Santi Cazorla and Lukas Podolski (to whom fans have already taken). The team might not look as good on paper, but van Persie is no longer worth the headache.