Some exchanges have not, and have no plans, to give access to coins from bitcoin forks. Many of them are already worth a substantial amount of money, and likely will increase in value. Is there a legal basis for suing exchanges to get access to such coins?
Since the exchanges are acting as custodial agents, they are holding bitcoin on behalf of the user, just like a brokerage does not "own" the stock but holds it on behalf of the customer. Whether or not the exchange plans on spending that bitcoin, if they do not give it to the customer they are stealing from the customer. Since coins from bitcoin forks are associated with the private keys held by the exchange, the exchange cannot argue that they did not "claim" them by taking no action, because they do own them, whether they wanted to or not.
I could imagine people pooling together to sue exchanges if this argument is viable.
First of all, you are comparing an unregulated enterprise with another enterprise that is operating in a regulated atmosphere. For the fact that exchange sites performs the similar functions as that of a brokerage firm does not mean they are the same or they should be forced to comply with the same rule especially as it applies to regulations and performing a specific function.
Again, a lot of exchanges would issue a statement on their support for a particular fork or otherwise and would advise users to act on such. If your exchange site is not supporting your preferred fork, you have the option of moving to another exchange. I know Yobit is one that support even nonexistent forks. Another option is to keep in your own wallet then claim at your pleasure.
Whether you can sue or not, is not negotiable but whether the judgement will be entered in your favor is another thing entirely that would be decided by the learned judges.