Figuring a Sidechain blockchain that has high capa and low confirmation time like ETH for example. Call this sidechain "RSK" (rootstock) for example.
High capa means lower decentralization and lower RX fees. 2-way peg with BTC means 1 mRSK = 1 mBTC.
Assume adoption increases, so TX fees on Bitcoin increase further. People will start buying mRSK with fiat directly, so they save the bitcoin network tx fees. RSK will have same utility as BTC except lower TX fees, i.e. higher utility after all, as it used to be when fees of BTC were still low.
But most Bitcoin in circulation is still on BTC not RSK blockchain, so RSK shortage, hence RSK price rises due to increasing demand. So does BTC price, due to the 1:1 two-way peg.
Some people earning many mRSK will turn them into mBTC via 2-way peg on-chain for savings purposes – Bitcoin is more secure than rootstock blockchain, but only if it is worthwhile, because otherwise Bitcoin TX fees are too high.
People who still have Bitcoin savings on an exchange and want to buy a coffee from that will turn some of their mBTC into mRSK. But not via 2-way peg, because that is too much TX fee. Instead, they swap them on the exchange, off-chain, because that is much cheaper for small amounts! Only for big amounts, using the 2-way peg is cheaper.
Market forces and arbitrage will yield a balance of exchange rate near 1:1 on the exchanges, a suitable TX fee on BTC, a suitable TX fee on RSK, and a suitable amount of RSK in circulation, and a suitable mRSK price = mBTC price
The new crypto coin of utility is RSK.
The security of RSK is about the same as the security of Bitcoin Unlimited would be with the same blocksize and capa.
BTC has highest security because of high decentralization due to still small blockchain, while being the backbone for the much more powerful (utility!) RSK network.
Exchange between RSK and BTC can happen on-chain via 2-way peg or off-chain on exchanges, where x-rate will be close to 1:1, because otherwise arbitraging using on-chain 2-way peg will avoid too much deviation of 1:1 exchange rate.
People get used to using mRSK like cash in earlier times for spending.
People get used to using mBTC like bank deposits in earlier times for saving.
People get used to transaction fees when changing between mBTC and mRSK, like ATM withdraw fees in earlier times.