It seems, however, like there's finally movement happening.
An April 27 update to the Cortana support page actually mentions Alexa. "Cortana and Alexa are still getting to know each other. Soon you'll be able to ask Alexa to buy things, add items to your shopping list, access your Alexa skills, and more," says the brief update on the page. Yes, "soon" is vague. But it's something.
Typing "Alexa" into the search box in Windows 10 (on the Fall Creators Update version, at least) yields a message saying "I'll be able to connect you to Alexa soon. Stay tuned!"
Last summer, Amazon and Microsoft announced that their respective personal assistants would be able to talk to one another, so customers could opt to use the assistant most suited to a particular task. Amazon and Microsoft officials said last year that they'd make Cortana-Alexa integration available before the end of calendar 2017. Since then, there's been no update on when this might arrive.
In early March 2018, Cortana team members told Windows Insiders that the Cortana-Alexa integration was in "internal self-hosting" at Microsoftat the moment. Microsoft is working to "make sure it's (the integration) a great experience," the team said, noting that bringing together the two different speech stacks is "non-trivial."
Recently, Cortana's new boss, Javier Soltero, admitted that "skills for the sake of skills won't fly." He told PC World that skills usage isn't "quite as deep as most people think it is." He also acknowledged Microsoft's in total catch-up mode on this front. (That's for sure, with Alexa at 40,000-plus third-party skillsat last count.)
Given Cortana is set to access Alexa skills via this integration partnership, maybe Cortana's skills shortage is less horrible than meets the eye.
Soltero also declined to say whether there are any other Cortana-powered speakers in the works. Currently, there's one from Harman-Kardon. I think speakers might not be where Microsoft is focusing; perhaps it's more about conferencing systems, microphones or other more business-centric peripherals.