I don't think that there is an explicit link between this and the usability of your browser here. I simply think that a convergence in terms of UI elements helps both the developers and the marketing, the branding of the company.
Pretty much any mobile user has a computer, and viceversa; so there is an high probability that using 2 different environments from the same brand can destabilize the idea of the user about a given brand. Having 2 identities is like having almost none because you are confusing people, it always helps to clarify and unify the message, plus if you consider the human brain as a computer, anything that requires you to "think" is a requirements that brings you from your habits/subconscious to a more conscious status, thus ruining the "magic" of the UX of that brand . If you are forced to think or you receive any input that makes you aware of what you are doing you are using the computer with that UX as a tool, a that's really bad because that UX will have no special appeal to you and there are lot of tools on the market.
There is also another idea that I personal believe is true, at least at some extent, and is about the concept of "size".
Have you ever took a picture where there was a clear subject in the frame but no references around to get an idea about the size of your subject ?
Like when you take a picture of a wheel alone on a flat background, and you just see a black circle with some metal in it, how your brain can get an idea of the approximate size ? Well the answer is simple, it can't. Unless there is something that you can track to get a reference, like a bolt or screw, or something from the environment around it, your brain is processing the image of a generic circle composed of some generic materials and that's pretty much it.
Good panels for displays are pretty expensive, at least for the customers, the Apple lineup ranges from the extremely cheap TN panel on the Macbook Air family, to the "Retina"s on ipads and macbook pro .
Probably Macbook Air don't like to be reminded of the fact that on their own machine pixels are that big, that will not help Apple for sure, plus you can't always measure everything in pixels, and you can actually benefit from removing the reference that ruins the magic about your screen resolution.
One classic example of that are videogames, and on some extent videos or content like that. If you play a game on a 13", you are probably getting the same experience no matter if your machine mounts an expensive panel or not, unless you go really low on the specs, you can maintain pretty much the same experience, the same visuals.
The web of today is filled with content that "scales" or with content that will not be much different if played on an high end or low end machine. The concept of the size is more "relative" to the content rather being strictly related to the number pixels offered by your monitor. Lucky for us the time of the Verdana at 12px is over and today scaling technologies or nice fonts expressed in pt are way more popular.
Last but not least, the scrollbar is not for input anymore, historically the scrollbar was serving at least 2 purposes:
- output: informing the user on where he is on the page
- input: drag the bar and move vertically or horizontally
Of course since touch devices are quicker in doing the last part, this is natural selection and scrollbar just lost 1 of the 2 functions, the modern way of packing content usually does the rest to minimize the utility of the first function too.
On mobile devices the screen is also a giant source of inputs, you probably don't want a scrollbar monopolizing the UX of both the browser and the main OS that only get in the way.