Asking because you seem to Have Great Thoughts On Fun Media but do we ever see Ed and Izzy actually enjoying each other's company? Is your reading of their relationship a mutually beneficial teamwork thing, or are they actually friends on some level?
Oof, Anon this one is tough for me. I find Izzy fascinating as an antagonist, as a mover of the plot, and as a voice of reason. From a shipping angle (somewhat unrelated, I know) I only see Izzy/Ed as a bellwether of something having gone deeply wrong, as I think a relationship between them, at least as we see them in the show (as opposed to a flashback to the early days which would theoretically contain a dynamic we haven't seen), would be deeply toxic. For example, I would see a Izzy/Kraken!Ed sex scene in S2 as Ed hitting his lowest point, absolute rock bottom of despair and toxicity, in the same way that I would see Stede making a sincere attempt to be Mary's lover and fit into his old life--had she been more receptive to also trying to "make it work" when it would kill them both spiritually to do so (ie, I would be screaming at the screen "No! God no! Oh god please no! No, no, nooo!" ala Steve Carrell in The Office).
I don't feel I've actually formed a coherent opinion about whether or not Ed and Izzy are friends though. As a character functioning within the plot, I think Izzy sees himself as what would be a modern agent to a rockstar for Ed. Basically, doing all the day-to-day stuff so this creative genius can be free to do their thing. But when that creative genius won't do the very basics of making sure the sweet deal they've got going continues (like say, showing up for an autograph session on time, or failing to make a plan so they survive an encounter with the Spanish) then that relationship becomes strained. As I've noted elsewhere, like a rockstar agent, Izzy feels possessive of the "brand" of "Blackbeard" much like a successful agent of an individual star who is also a brand (like Elvis, Elton John, Mick Jagger, etc) would but it would be a thorny sense of possessiveness because "Blackbeard" is kind of a band name for Ed but it's also actually his identity that Izzy feels possessive about. It gets muddled with Izzy doing the work to support this brand, with Ed working to support this brand, but also with Ed being this brand. So Izzy is kind of right to feel protective of that brand but also very invasive for doing so.
Now, have Ed and Izzy ever been friends? Have they ever enjoyed each other's company? Izzy clearly enjoys a degree of familiarity with Ed, he calls him Edward and Ed (something Calico Jack said Ed would literally murder others for doing) which IMO means he's clearly in Ed's close confidence. But, I don't think Ed sees them as equals.
Ed treats Izzy as an employee, to my eyes. A very useful employee. One he literally can't do without and that he trusts with his most important jobs. But still an employee. Think back to him sending Izzy against the man's protests to go fetch Stede himself, Ed ignored Izzy's protests because he wanted the job done right.
Later, Ed sarcastically mocks Izzy for complaining that his job has been hard (something an employer might do, but not a friend). In the same breath, Ed indicates he feels disdain for pirates in general, even those on his own crew, as he seems to see pirates as people who have chosen a life where if they die they knew what they signed up for and don't deserve to be mourned. Possibly as terrible people who have chosen this life, so he has even less sympathy, if my read of his emotion being disdain in that scene is correct.
By the time we see Ed, I get the distinct impression that he finds other pirates repulsive unless they're "doing something original" like Stede. And, without much evidence other than reading between the lines, I'd hazard that Ed's view of pirates might go back all the way to when he first became one (or before). Becoming the best at something doesn't mean you respect your peers. If anything, his own success as a pirate, the close view it gave him of how other pirates behave, may have only deepened his disdain for pirates. After all, Ed doesn't kill and he relies more on fuckery than on brutality (except for maiming) so to his eyes, other pirates might seem a brutish, violent lot not worthy of his time let alone his sympathy or interest.
And Izzy is a pirate. A smarter pirate than the average and able to help Ed's enterprise function, but one who also lacks originality and creativity. Izzy IMO is not spared from being in the group that contains Ed's low view of "[no one] doing anything original out here." Even when asked to do basic creative interpretation like describe the shape of clouds, Izzy is too mission-focused and pragmatic to do anything but bore Ed. And before we say that Izzy is right and Ed is wrong at that moment to be so mission-focused, Izzy didn't do fuck-all to save them from the Spanish that night. It was Stede and Ed's (and Stede's crew's) combined creativity and skill that saved them with the lighthouse fuckery. Izzy appears to have vanished. At the very least, he didn't contribute to the actual saving of the ship that he kept giving Ed so much shit about.
Tragically, I do think Izzy thinks he and Ed are close. I think being the top employee of a creative rockstar like Ed has given him the false impression that he's Ed's friend, rather than that he's friendly with Ed as an employee. (Remember, kids, your company doesn't give a shit about you and will fire you whenever convenient to them, no matter how loyal you are. In this instance, Izzy is the employee and Ed is the company that creates "Blackbeard".)
Ed has let Izzy into his confidence, but as an underling. Izzy thinks he's earned more than that, that he is more than that to Ed. I don't think Ed agrees. Izzy thinks they're partners and Stede is stealing Ed away. Ed sees Izzy as a useful assistant.
Izzy's ability to force "Ed" back into being Blackbeard, or rather the Kraken version of Blackbeard that might be more than Izzy bargained for, is not a result of Ed respecting Izzy. I vehemently disagree with interpretations where Ed's reversion to the Kraken is as a result of Ed being afraid of Izzy. He's never shown any fear of Izzy. Rather, I think Izzy is the annoying alarm clock. He's the harried assistant who has been calling the rockstar every day while he's on vacation and finally shows up to the beach with a clipboard to say time's up, you've got to come back to the real world now. Ed resents Izzy. He resents Izzy's presumed familiarity that he could threaten Ed or assert any kind of power over him and therefore Ed maims Izzy to reestablish the hierarchy.
Were they ever friends? At most, I think they were friendly. I think Ed had a point where he was pleased to discover a fellow pirate who could get shit done, who could function, and worked well with him anticipating his needs and taking care of the grubby parts of the job (including managing the pirates that Ed disdains) so Ed doesn't have to. I could see him being warm to Izzy, charming as he often is, in those early days. I can see that warmth and charm coupled with Blackbeard's terrifying competence, become that heady combination that can only be described as charisma making Izzy feel fortunate that he's allowed so close to the star of the show. I can see that excitement fading into the humdrum of everyday life where he's less awed by Ed and more frustrated when Izzy is called upon again and again to be the voice of reason, to do the grubby job.
I can see Izzy not understanding that no matter how hard he works, he will never be seen as Ed's equal because the way he functions is as a subordinate. He would have to break out of his old habits and become a rockstar in his own way to win any respect or interest from Ed.
Ed respects fellow rockstars: Calico Jack, the Gentleman Pirate, Jim - all self-assured people with their own brand who don't care what the world thinks. Izzy doesn't function that way. Izzy is an assistant, an enforcer, an employee that Ed would desperately like to have some fucking creativity and personality of his own but because he doesn't, he will never rise to be more in Ed's eyes.
And that's my long-winded two-cents ;P