Making attributes and properties symmetric to one another would be difficult for...

Making attributes and properties symmetric to one another would be difficult for the existing DOM API: methods like `addEventListener` are (prototype) properties on individual DOM elements, but would be nonsensical string attributes. Making your idea concrete:

    // our document is like:
    // <foo bar="asdf">
    let foo = document.querySelector('foo'); 
    console.log('bar', foo.bar); // cool, prints asdf
    foo.bar = 'nice'; // <foo> element is now <foo bar="nice">
    foo.addEventListener('some-event', e => console.log(e)); // wait, what?

So DOM element methods would instead be free functions like:

    HTMLElement.addEventListener(foo, 'some-event', e => console.log(e));

It's a matter of taste, but I for one appreciate having object method calls in JavaScript.