Jeff Lynne and ELO are two separate entities in MB. Of course they are divisible. They are already “split”. I don’t understand your argument.
It is possible that an editor would wish to create a third inseparable artist, “JL’sELO”, distinct from ELO. But this hasn’t happened, has it?
You just used Simon & Garfunkel as an example an artist that can’t be split. How exactly is “Jeff Lynne’s ELO” different?
“S&G” is a third entity, distinct from “PS” and “AG”, As a duo, they have relationships that don’t apply to the individual collaborators. If “S&G” were to be split, MB would lose information, like e.g. the discogs page rel.
“JL’sELO” on the other hand is not a third entity distinct from “JL” and “ELO” (or if it is, I don’t see it on MB). One could make a case that it should be.
If “JL’sELO” were a third entity in MB, and somebody was wondering “should I split it?”, then they would apply the test that you mentioned. That is, they’d ask “does JL’sELO have any relationships that can’t be applied to either JL or ELO?”
Hmm. I like to think that I’m pretty good at spotting the source of miscommunication, but in this discussion I really don’t understand at all where the disconnect is.
I see what you’re saying, I just don’t see how it’s relevant. Losing data is a valid reason for not splitting S&G, but it’s not a reason that we should split bands that don’t fit that model. Another valid reason for not splitting S&G is, like Jeff Lynne’s ELO (and all the other examples I gave earlier) is that they’re one band, and we don’t have a good reason to split one band into tiny pieces just because we can. We’d end up with two or three different MB artists pointing at the same single artist on other sites, an artist’s page wouldn’t list just their solo releases, and releases would appear to be temporary collaborations when they aren’t.
The reason Simon, Garfunkel, and Simon & Garfunkel are three separate MB artists is because Paul and Art can work independently, or together as something distinct from their solo work – there are three actual entities that you’d file three different places in a music store. Jeff Lynne’s ELO is still just the current name of ELO, and that’s the reason we wouldn’t create a third artist for it – there’s not a music database out there that considers “Alone in the Universe” as not part of ELO’s discography, or considers Lynne’s solo albums as part of it. Jeff Lynne can work independently of ELO, but ELO cannot work independently of it’s own members. The only way it would make sense to link Lynne’s name separately is if he wasn’t part of the band. If Art Garfunkel didn’t have any solo releases, we still wouldn’t format those albums as “[Paul Simon (as Simon)] [Simon & Garfunkel (as & Garfunkel)]”, because the band has relationships that Paul Simon as a soloist does not. It’s the same case with ELO, just like with any other “Leader + Band” vs “Solo Leader” scenario.
I want this to be the case.
Breaking free from the limited cataloging capabilities of a physical music store is great, makes related artists easier to browse, and doesn’t make a jot of difference when tagging (unless you want to make use of it).
And if an artist doesn’t want something to show up in their discography they really shouldn’t put their name on the front cover 
This is exactly what @CallerNo6 was saying -
In these examples, for instance if you split up [Jeff Lynne] & [ELO] this doesn’t happen. The ELO page contains ELO’s relationships, Jeff Lynne’s page contains Jeff Lynne’s relationships.
We haven’t lost either, and none of them are doubled up.
If there was a specific relationship dedicated to ‘Jeff Lynne’s ELO’ (not ELO or Jeff Lynne), then CallerNo6 is agreeing that you shouldn’t split them - but that should possibly be a third artist because it is now distinct from ELO.
I don’t know if that was helpful or if I was just repeating things… worth a try I guess 
That’s fine, but that’s only achievable through relationships, not through ACs. (I’m surprised there isn’t already a page that shows all releases a person appears on as a bandmember – probably a script could do it). If you tried doing this through ACs for Lynne, you’d end up with a page of his two solo albums and the one (so far) ELO album where they went as “Jeff Lynne’s ELO”. The page wouldn’t include anything else from ELO, Travelling Wilburys, The Move, Idle Race, etc. Manfred Mann’s page would be an even bigger catastrophe. Even Paul Simon’s page still wouldn’t list his Simon & Garfunkel work. Tagging would be broken for people who use the “use standardized artist names” option (unless we used 's as a join phrase), searches would break, and there’d be no way to implement the rule consistently. Can you give me an example of how you would write the style guideline that an average editor could read, understand, and follow correctly?
I assume you’re being facetious, but there’s clearly a good chunk of the time where the artist has no control over that. Take a look at the compilations on Peter Green’s page.
Currently there’s only one album credited to Jeff Lynne’s ELO, but imagine he does seven more like that. If a user sees eight albums on Jeff Lynne’s solo profile that aren’t on his solo Discogs, RYM, AMG, Wikipedia, etc. pages, something’s wrong. If I go ahead and link to those profiles (because they should be linked if they represent a significant chunk of what’s shown on his page), those profiles are double-linked and, even though only part of them would be applicable. So either Jeff Lynne’s page wouldn’t contain the relationships necessary to cover the releases on his page, or it would contain duplicated relationships, some of which only partially applied. Somebody like Manfred Mann, or any major jazz figure would have six or seven links to databases for each of the different ensembles they led.
I still haven’t heard any reason why “one band, one link” doesn’t work.