Say a microtransactions sidechain is developed with a fixed supply of one-billion Micros, and an exchange rate of 1 BTC = 1 million Micros. That means that 1000BTC *total* will ever be able to move to the sidechain. Say the sidechain is very successful; ie, Micros work really well and start to gain a lot of real-world economic traction and value. So the 1000BTC gets transferred over.
Now say that Micros continue to see more use. Their purchasing power goes up, but this has no effect whatsoever on the purchasing power of bitcoin because the max has already moved in. Now all we have is another alt that *used to* have an easy decentralized way of buying it with bitcoin.
Arbitrage. For example: All 1000 bitcoin are transferred and micros increase in value to the point that:
1 million micros = $800
1 bitcoin = $400
Anyone wanting to arb this spread can sell 1 million micros for $800, buy 1 bitcoin for $400, pocket $400, convert that 1 bitcoin to 1 million micros, rinse and repeat. Most likely, one billion micros will never be in circulation at any point in time because of arbitrage.
What if the exchange function specified that after time/block N, the exchange rate is 1 BTC = 0 Micros ? No more arb.
Not to be pedantic, but the point is that the exchange rate can be defined by "any deterministic function". Seems to me that there are probably many classes of deterministic functions which could prevent value from moving back to bitcoin.