Well, really, the problem is that JimBob is in total control of the interaction here. Maybe your bank says, "Sure, here's an affidavit showing you had $30,000 on date X", but that's not good enough for JimBob; he needs to see the actual, physical bills and needs proof that _those specific bills_ were in your bank's vault at the time.
This process puts a fair amount of burden on the "bank", because they need to deal with JimBob's byzantine lollipop claims process _directly_ with their own cash, rather than issuing a standard affidavit that'll work equally well for MarySue's pop-tart claims process. Or, in more technical terms, _every time_ anyone comes up with a new coin, coinbase would have to dust off the cold vault, generate the proofs of ownership, reassign them to the new owners, then move the bitcoin over into newly generated cold addresses to restore the security posture of the cold vault coins.
Moreover, creating new types of altcoins is a process that can be easily automated, and at little cost to whoever is instigating this creation process. Of course, most of these coins won't ever gain any popularity or value - but then what's the threshold? At what level of popularity does a broker need to do anything? What happens if a coin is totally unpopular initially but gains popularity later - do brokers need to backfill? What if the key material has been rotated away and destroyed in the meantime?
For that matter, how do we measure popularity? Volume? It's easy to spam volume if you control the first exchange for your altcoin. Market cap? It's easy to fake market cap and unrealized gains when nobody can transfer coins yet. Hashrate? Who knows when that'll settle down. In any case, it's not the sort of thing that can really be objectively determined too quickly after a split.
These don't become an issue with normal securities because, in normal stock market securities there is only one authorized issuer who is able to issue splits, and this issuer incurs real, significant administrative costs for doing so. They also must involve credentialed third parties, and all participants face regulatory scrutiny, fines, or even jail time if they deliberately set out to abuse the system.
Compare to the creation of an altcoin, where the costs of creating a new altcoin are tiny, but the costs of dealing with the fallout by brokers can be quite large. And, of course, there is effectively zero regulation that would give penalties to deliberate abusers. There's therefore a large cost and risk imbalance between altcoin creators and brokers who have to deal with the new altcoins. This sort of cost/risk imbalance results in, effectively, a sort of denial of service threat against bitcoin brokers if it's allowed to stand.
For this reason, the precedent set by this split is going to be of great importance in the future of bitcoin and altcoin brokers - if brokers must deal with splits, it will mean that they will need to segregate coins and keep them online ("hot") at all times in order to be able to deal with any split immediately and/or retroactively. This in turn will hurt the security posture of these currencies substantially. The risk of screwing a split up will also hang over any service that holds *-coins on behalf of their customers or other third parties.
This will also impact the legal feasibility of off-chain transaction aggregation schemes (e.g. lightning) not feasible, as there's no guarantee that the next harebrained altcoin split will be able to deal with redeeming the complex transaction scripts involved with e.g. an unsettled lightning channel - and if it doesn't, who is liable?
So, in short, _requiring_ brokerages to deal with altcoin splits and redemptions opens up a huge legal can of worms that is probably best left closed, for the viability of the overall altcoin landscape. Yes, it sucks that coinbase didn't do something for this particularly public split, but if they did they'd have to be processing splits every other day, or perhaps even more frequently.
Disclaimer: I have no position, long or short, in bitcoin or any other similar "altcoin" assets, nor do I have any plans to open such a position in the forseeable future. However, I do find it fascinating to watch this legal/economic experiment evolve from a safe distance.