I think there are a few things at play here. First, is people want this functionality. Second, they're likely getting some funding from MS for doing this (Cyanogen OS, similarly is about making a living, or profit for that matter). Third, Google's integration from Apps, to the Play Store comes with a lot of strings attached, and it makes sense for Cyanogen to avoid as much of that as possible.

Personally, I want as close to a pure android experience as possible, and may move from the OnePlus One to whatever the next smart phones from Google/Nexus at the end of the year are (or current if my phone drops). The only thing I really like about my OPO over others, currently is my back cover is the bamboo option, and I really appreciate natural/wood when it's available for a product.

I agree completely. I don't see any justification for doing this, and it just further confuses and adds complexity to the user experience. MS/Cortana will never be able to offer as deep integrations across Android as Google does with Now, and that gap's only going to continue to grow as more 3rd party devs create Now cards and Now intents within their apps. I don't see that happening at all with Cortana.

I'm using an Android Phone with mostly Microsoft apps: Outlook, OneDrive, Skype, OneNote, Account App, Health, Excel, Word. For me Cortana integrates better compared to Google Now, as it can access my information.

Why not? Remember, this is Cyannogen's distribution, so they could change it up so that the things that would be answered by Now are answered by Cortana. Now cards might not carry over, but that shouldn't be a big deal. And Cyannogen should be able to make Cortana respond to the Now intents.

Indeed, Cortana's integration with Windows Phones is quite similar to Google Now's with Android. At least as far as the APIs which are open components of Android, rather than proprietary Play services, Cortana should be able to pick up the same intents and all.