I think you're putting together an interesting theory, but it's certainly not one that people ignore. Far from it! Pretty much any take on the situation that isn't the most simplified and child-friendly gets into the fact that Henry VII and the previous generation had been involved in the Wars of the Roses over the crown of England, and that a huge part of the reason having an indisputable heir was important to Henry VIII was that the Tudor dynasty was fairly new to the throne and needed a stable succession. If it seems that people are ignoring this, then I think you might need to find more informed people to talk about the Tudors with or better books to read. (Sorry.)

However, I think you are misrepresenting things a bit.

Henry had the task of holding together a family that just two generations before was slaughtering each other in the literal streets over claim to the throne. His mother and father are the marriage that brought the Plantagenet fighting to an end. It was all on shake-y ground however because he lacked an air.

The marriage of Henry VII and Elizabeth of York was a brilliant bit of alliance-making and political theater, but it's not correct to present it as THE event that ended the fighting - in large part because there continued to be rebellions in favor of Plantagenet heirs even after Henry's coronation! To steal a chonk from a previous answer of mine: the Stafford-Lovell Rebellion in 1486, which was small and resulted in the execution of Sir Humphrey Stafford; the pretender Lambert Simnel in 1487, whose loss at the Battle of Stoke resulted in the deaths (in battle) of Francis Lovell and John de la Pole (a descendant of Edward IV); the pretender Perkin Warbeck in 1495-97, which resulted in the executions of Warbeck and Edward Plantagenet in 1499. Henry VIII dealt with the last potential Yorkist heirs, executing Edmund de la Pole (John's brother) in 1513, Henry Courtenay and Henry Pole in 1538, and Margaret Pole in 1541. Even outside of this issue, the death of Richard III in battle was a bigger factor in ending the fighting. Henry VII was actually quite careful not to present Elizabeth as "the Yorkist heir", and many historians have interpreted the lateness of her coronation as queen to Henry deliberately distancing her position from his own and making it clear that she was queen because she was his wife, not because of her own descent.

This is a great example of contingency, "the absence of certainty in events". Had any of these rebellions succeeded, yes, perhaps there would have been continued instability and fighting between Yorkists and Lancastrians; on the other hand, maybe they would have been more stable than the Tudors! The Tudors, after all, were very tangential to the Lancastrians, barely even eligible for the throne (if they were at all). I have another answer here about why Henry VII's claim on the basis of blood was problematic. The short version is that there was no true Lancastrian heir after Edward of Westminster, son of Henry VI, died; the reason that Henry VII became the leader of the Lancastrian cause is as much (if not more) from his paternal descent from Henry VI's non-Lancastrian half-brother as it was his mother's descent from Edward III. The Plantagenets weren't "slaughtering each other in the literal streets over claim to the throne" like characters from A Song of Ice and Fire competing to play the game of thrones - they were solely interested in competing with the Lancastrians, whom they viewed as usurpers for, uh, having blatantly usurped Richard II. If Henry VII had failed and Richard III's nephew Edward (for instance) had made it to the throne, there would likely not have been significant Lancastrian resistance. We should probably look at all of the rebellions against the Tudors, and the executions they committed against actual or potential Plantagenet claimants to the throne, as evidence of the tenuousness of the Tudor claim in the first place, rather than as evidence of how England was doomed to continued civil war if it weren't for Henry VII and Henry VIII holding onto the throne.

As a non historian but avid reader I’ve pulled together that Henry had to produce an heir to hold the kingdom together. He respected Katherine and knew she didn’t want bloodshed so he let her live in isolation/exile as was the way for many a monarch who didn’t want to instigate a war but didn’t have any use for them. Anne came from a political ambitious family. One that could’ve plunged England back into chaos had be allowed her to live and have access to Elizabeth. I feel this was the case for any of the wives he beheaded. It wasn’t this (now sexist) idea of needing a suitable wife. It was he needed an air at any cost and women w an agenda were not the ticket.

Henry VIII needed a male heir for what we might call propaganda purposes, which I discussed in this answer on why he married "old" wives and this one on infertility: he needed to show that God was blessing him with sons because he was the rightful king. He didn't literally need a male heir to hold the kingdom together, though. He could have simply made Mary Princess of Wales (he would eventually add her back into the succession, so he wasn't completely unable to countenance a queen regnant), or allowed the throne to travel down the lines of either of his sisters' descendants.

I don't really understand where you're getting what you're saying about Katherine of Aragon here - what bloodshed are you suggesting he was avoiding? He had absolutely no legal cause to execute her, she was massively popular with the English, and he likely had some remnants of sentiment from their long marriage. He was willing to let her go into retirement and live as Dowager Princess of Wales because that was just as good as anything else, if she had accepted it and stopped insisting that she was legitimately married to him.

I also don't understand what you're suggesting about Anne/the Boleyns and Elizabeth. If Elizabeth were acknowledged as heir or if Anne had had a son after her, the Boleyns would have had every reason to support the Tudors. They were ambitious, but ambition within England (outside of extraordinary circumstances) meant playing up to and achieving favor under the sovereign. Katherine Howard's death (as I discussed in this answer about her execution) was likewise not about the Howards/Boleyns being a danger to the throne, but solely over Henry's concern that she was unchaste.

Henry's problem was that he wanted a wife to provide a son (or preferably multiple sons) and have absolutely no taint about her to reflect poorly on him/his reign - which, to be fair, was what all kings of the period wanted. Anne Boleyn and Katherine Howard were both accused of adultery, which was the absolute worst taint for a queen. Anne of Cleves had the whole "omg I know she's not a virgin because her breasts are too big" thing. Katherine of Aragon was great at being queen, but couldn't give him live sons or sons who lasted past childhood. The distinction from other kings was that his court was so unstable that accusations were able to be made in the first place against his wives and taken seriously, and it was so unstable largely because of his own actions in starting the English Reformation rather than because of the Wars of the Roses.

A good read. Thank you for answering. The murdered in the streets refers to Edward IV dragging someone out of an abbey… didn’t the people think this basically cursed his reign in the eyes of god? He murdered someone in the streets on the steps of sanctuary.

Someone answered w what I meant by Katherine of Aragon.