TL;DR: Sidechains (if they succeed) force Bitcoin's hand, although decades in the future, in setting an inflation rate determined by the market, in order to tie miner's subsidies more exactly to the primary service they perform: that of securing Bitcoin's store of value. This is because successful sidechains would allow Bitcoin transactions to be disconnected from Bitcoin miners. Bitcoin therefore could not rely on transaction fees for its network security incentives. Sidechains would have made it clear that transaction functionality is not intrinsic to or inseparable from the Bitcoin network; only the store of value function is, and therefore miners must be continually rewarded for maintaining this function alone, for the lifetime the network.
Thanks for distilling the concern.