It's because there are well established ways to interpret "militia" and "the right of the people to keep and bear arms" that draw on institutions and approaches that had been in place for hundreds of years by the time the 2nd Amendment was written. We are not actually ignoring the "well-regulated" part. The amendment enables the militia, it doesn't define it. It is for other laws and institutions to actually sort out how militias work (the Militia Acts of the 1790s, groups like the
https://www.missourimilitia.com and so on). You can't have a militia without private ownership of and relatively free and easy access to weapons.
Today, we use "militia" to mean any unofficial group of armed people, but the common law militia was and is (it is still part of the laws of the USA, see 10 USC § 246) something more specific. The idea is that every potential lawful combatant -- every free man neither too old nor too young to fight -- could be summoned and they would supply their own weapon, clothing, and other supplies. The authorities did not expect to have to supply these things; people were supposed to have them already; and these people were not professional soldiers, with security clearances, government jobs or something like that. They were just regular citizens.
Now, what if they tried to make some kind of law like, only people officially registered in the militia can have guns? This creates a tremendous enforcement burden and does not serve much purpose, because militia membership is supposed to be something that's extremely widespread and so guns would be all over the place. Such a rule would have run-up against another factor, which is that many people who might have been technically too old or too young, or even not eligible at any age because they were women, would still have other reasons that were perfectly reasonable for using guns -- like hunting and shooting pests around the farm. If you see a non-eligible person with a gun, it does not necessarily mean anything; maybe the gun is their dad's or their husband's or their son's; hard to say. It's not really sensible that someone in the same house, and sort of the same legal person due to coveture (the merging of a woman's legal personhood with that of her husband), could not use or put hands on the gun. Enforcing any provision like this would have been extremely tedious and involved, given that the militia relied on people storing and maintaining weapons in their homes. It would, I think, result in something that everyone familiar with the Anglo-American legal tradition, in those times and in ours, would recognize as government overreach.
In fact, the situation was that people had arms for many purposes in England and the colonies, not just for militia purposes, and this was a social institution that went back to at least the 900s in England. The militia as an institution relied on the institution of private weapon ownership, but private weapons ownership was independent of the militia, and people treated weapons like any other article of private property -- they were free to modify them, sell them, and assign them in their wills.
That's why we interpret the amendment the way that we do: in order to have a functioning militia, people need to have weapons and be familiar with them. The militia relied on a prevalent social institution of private weapon ownership: "the right of the people to keep and bear arms". The 2nd Amendment says, more or less, that obstructing private ownership of, commerce in and training with weapons would undermine the militia, and so such obstruction is prohibited.