Quantum computing isn't a threat. it will just mean mining will be much quicker. Either way, it's some time away, and Bitcoin will no doubt adapt to any challenges that Quantum computing poses. let's not forget that bitcoin core blockchain is essentially software that is still being maintained and improved.
Miner's abandoning bitcoin can be a threat. the difficulty algorithm adjusts every 2016 blocks to maintain the pace of the blockchain so to speak. however, if such an attack by miners were to occur right after the adjustment, and the majority of the hash power were removed, it would theoretically take an infinite amount of time before the next 2016 blocks are reached. This is what happened when BCash attacked BTC a few weeks back - that's why transactions slowed and fees increased. thankfully enough miners hung around to keep it ticking along and eventually the miner's came back when the so called "flippening" failed.
But without that quantum computers the mining will be too slow to carry-out the heavy load of transactions and mining activities - as a result, single transaction will take forever to complete since there will be a pile-up of data on the blockchain.
i'm not quite sure i get you..
anyway, data theoretically shouldn't pile up on the blockchain, because the difficulty algorithm should adjust to make mining easier if it starts to head that way.. but like i said that only happens every 2016 blocks.