That would most certainly lead to a huge spike in on-chain transactions since transactions inside these wallets are mostly off-chain
Off-chain transactions occur only when people move funds from one Xapo wallet to another Xapo wallet or from one Coinbase account to another Coinbase account. Everything else not contained in the same proprietary wallet eco-system needs to be broadcasted on the Blockchain like foreign outgoing and incoming TX
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A collapse is a bit too much imo.
It would would however force a much faster implementation of a solution and it would cause all the parties to agree on something eventually as there is no more time to keep fighting over the best solution.
With the increasing interest in bitcoin, I do think something like this may start to occur sooner rather than later.
There may be a total chaos coming on if something like that happens for real. In real life, though, it is more likely that events like what happened two days ago will just start happening more often, and people might get eventually accustomed to them, at least, to a degree, either having to wait and maybe resend their transaction a few times after it gets dropped or pay substantially higher fees if they want it to be processed "sooner rather than later" (that would be miners' paradise and klondike all in one)...
In this case, we would probably witness a phenomenon known as the
boiling frog