Copyright is really an orthogonal concern here. Yes, it certainly endows Disney with some rents that they shouldn't have, but their dominance is based on a continuous supply of new content, not derivatives of Mickey Mouse.
Not surprisingly, non-character stuff tends to be way better quality.
We do have a few items from gifts over the years. Our 2 year old calls a gifted Minnie Mouse doll "Elmo". Makes me proud.
Monopolies work against a free market, as do barriers to entry. Businesses make more money if the market is not free, i.e. if others in the market are not free to choose competitors' products or to become a competitor themselves. The "invisible hand" is about reflecting pricing movement of free exchange, not enforcing the freedoms. If a society wants a free market, they need to set up rules that promote market freedom as a societal goal, which would (ideally) end up working against individual profit maximization (compared to a usurpable market) but for greater overall robustness and correction.
So economists have to weigh the disadvantages of oligopolies against the advantage of efficient production. For instance you wouldn't want several electric grids competing against each other. On the other hand oligopolies can have powerful lobbies distorting the political process.
It's a complex balancing act overall. If you're interested, this is a field of economics called "industrial organization".
1. Canada, for instance, has only 6 banks, none of which failed in 2008. The problem with banks is their being over-leveraged (that is taking excessive risks) and inter-connectedness, as well as human shortsightedness and managerial incentives encouraging excessive risk taking. The problem with large banks is generally their political power.
On the Disney topic their dominance doesn’t come from free-market but IP holding though. It’s a worse of both world situation where they fought hard to carve a protected niche for themselves.