Most of the current growth is due to empty one-minute blocks, which is not inherent in the design at all, and can (and probably should) be changed to a slower block target. For example, as I write this 5 out of the previous 6 blocks are all empty:


Very little of the actual current growth is due to the size of ring signatures. Increased usage will cause sub-linear incremental growth because the first thing that will happen is that empty blocks will have transactions added to them (reducing chain overhead from 100% to <100%) and the next thing that will happen is that block headers will be amortized over a larger number of transactions.

In some hypothetical future if XMR has transaction volume that is comparable to BTC, its block chain will be several times larger since its transactions are larger. If that happens, the market will have accepted that a constant factor (very likely <10x) of increased chain size is an acceptable trade off for increased privacy of transactions on the chain. I see no way to objectively predict whether that will happen.