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> there's no economic reason for them to stay in some balanced relation.

Actually, there might be. The fee needed to get a bitcoin transaction into the blockchain is determined by a market, and it is a flat number, not a percentage of the transaction. If bitcoin succeeds, it may not be practical to use it for smaller transactions.

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It's neither a flat number, nor a percentage. Fee is not hard-coded in the protocol, everyone can decide on the fee himself. Users decide how much they want to pay and miners decide how to prioritise transactions. The fee is freely floating in both LTC and BTC, no difference here. The only practical difference is liquidity and it is produced only by network effect which tends to create "one of a kind" winner in a competition between very similar networks.

If the maximum block size limit ever constrains the volume of transactions, what will happen to the fee people decide to pay?

Block size limit will be raised as soon as there's a pressure of transactions. Miners are not interested in devaluing their savings because Bitcoin is too expensive to use for newcomers.

http://blog.oleganza.com/post/43849158813/this-is-how-block-...

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