What's wrong with using the title attribute for accessibility?
The title attribute may not be read by all screen readers by default, if at all. Some will, but some won't.
Additionally, when users are keyboard only, touch input, or using voice access they may not have an easy way to view the content contained by a title attribute. Whereas assistive technologies beyond screen readers can make use of it.
Users with fine motor impairment may be unable to hover long enough to show a title, depending on their browser.
Labelledby has the highest precedence in parsing, and every screen reader will know what to do with it. It removes uncertainty as a dev -- you know absolutely what will be read by it.
Aria labels can be used to give blind users the same experience as sighted users, which may not be the same text as a tooltip. If you need to convey something visual about the item being labeled and some text, you can use aria attributes to provide that.
Title gets inherited by all children, unless a child has an empty title. This could cause weird behaviors for screen reader users if one isn't careful. Labelledby is not inherited, and gives you control over which specific elements get labels.
And the spec for the title attribute is for "advisory information", which isn't necessarily the same as descriptions. A title attribute could be used to give an image a credit, for example.
But the W3C recommends against relying on the title attribute for converting information:
* Relying on the title attribute is currently discouraged as many user agents do not expose the attribute in an accessible manner as required by this specification (e.g., requiring a pointing device such as a mouse to cause a tooltip to appear, which excludes keyboard-only users and touch-only users, such as anyone with a modern phone or tablet).*
You could argue that all the user agents across all mobile and desktop applications and browsers should present title information consistently even when there is no pointing device. But, that's unlikely to happen.
So you have a choice, leave out users with disabilities because "it's all the world's software that could change" or add a labelledby attribute and get on with one's day.