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.