Opinions on a single-tabstop split button?

On a call today, a design team was considering interactions for a combo 
button, also known as a split button. For this component, there is a 
primary action, along with a dropdown indicator (typically visually 
separated, to distinguish it from a menu button) which when activated 
exposes a menu of closely related actions.

Microsoft summarizes the intended use as follows
This control is useful for exposing closely related items in cases where 
an obvious default is available and where the individual items can be 
represented by an image, text, or both.
(
https://docs.microsoft.com/en-us/windows/win32/windowsribbon/windowsribbon-controls-splitbutton
)

My question to the group. Does anyone see problems with pursuing a 
single-tabstop interaction for such a web component?

The typical menu button has 3 keyboard operators (Enter, Space, Down 
Arrow), all of which do the same things -- reveal the menu. 
https://www.w3.org/TR/wai-aria-practices-1.2/#menubutton
What I'm exploring is that idea that for a split button, Enter/Space would 
activate the primary action, while Down Arrow would reveal the menu and 
put the focus on the first item (just like for a menu button). 

The advantage for the keyboard user is the elimination of a second tabstop 
for the second half of the button. Otherwise, the user is forced to have 2 
interactions across a single component. In terms of affordances, the focus 
would go around the whole button, both the primary and dropdown, making it 
clear that the interaction is holistic.

Does anyone have any concerns with such behaviour or the visual affordance 
for it?

Programmaticaly, I would think the button needs aria-expanded="false". I 
don't think it should have an aria-haspopup, for fear of confusing people 
who would assume activation causes a popup (as opposed to carrying out an 
action). Was pondering how to convey the idea of a split button. Obviously 
no role for that. There's always aria-describedby, but I was thinking 
possibly the dropdown icon could itself be given an ALT like "combo" 
"split" or "splitbutton" so that the user would hear '[name] combo button, 
collapsed'

Obviously we'll do some user testing on this, but I wanted to find out if 
anyone had explored anything similar or had opinions/insight.

Thanks!
Mike Gower