In general, yes, people should have their own Apple ID. They're free...why not? But two points to that:
1. When I had a work phone I used my Apple ID with that to load useful apps. This was allowed by my employer. I saw no need to go through setting up a new Apple ID for the purpose I needed it.
2. I NEVER had an issue with private texts sent to my personal phone appearing on my work phone, OR confidential texts sent to my work phone appearing on my private phone. This issue is apparently something new with IOS 12.
It's your decision if you want to use a personal Apple ID on an employer provided device. What are you worried about? Most employers do not manage iOS devices, and even those that do (like my employer) have limited visibility into the content on a device protected by an AppleID. We use JAMF (and to some degree Microsoft InTune). We can deploy apps to managed iOS devices, and we can see what managed apps are installed on an iOS device. I use a managed device (an iPad) and the JAMF administrator I work quite closely with is not able to see my messages or even the apps installed under my personal AppleID. I can manage InTune policies, but those are mostly limited to controlling how someone using an iOS or Android device (employer owned or personally owned) can access email and other content on their employer provided Office 365 account. About the most we can do with a managed device is to wipe the contents and set it up like new using a different AppleID. We can't access a managed device that is protected by an employee's personal AppleID without completely wiping the device.
Where employers run into issues with people using their personal AppleID's is when an employee uses a company purchasing card to purchase apps under their personal AppleID. Apps purchased by the employer should be purchased under an employer-based Apple ID that is able to provide either redemption codes for an app, or that is linked to a deployment tool like JAMF or Configurator.
I guess my point is that I would not be concerned about your employer being able to read your personal messages, but it's better to have a work specific AppleID if you want to keep personal messages off your work device for other reasons (maybe you share the device with others, or you just like keep your worlds separate)
While this may seem like an issue in iOS 12, it's only an issue for people who are doing something Apple has long recommended against: Sharing AppleID's. We are just seeing the issue crop up because Apple has implemented features and modifications that are more identity based than ever. Android users have the same problems when they share one Google account across multiple phones. My in-laws did this for years and it was so confusing because I never knew which one of them was texting me. Last year I finally helped them transition to individual Google accounts.