Similarly, if in the distant future some sidechain has 10x the funds going into mining than the Bitcoin mainchain, paranoid entities are likely to strongly prefer holding their funds in that chain, even at the cost of some dilution to their holdings (as long as the dilution is minimal enough - obviously there's a gradient).
If the security in the main chain is much weaker than on the sidechain, 51% attackers on the main chain can steal "frozen" coins, causing even more dilution on the sidechain whenever they do so. So people would want the main chain to be roughly as secure as the sidechain.