Does App transfer between developers necessitate a re-purchase by end users?
There's no 100% certainty here, but let me explain that because it's not as bad as it first sounds.

Assuming your Apple ID has previously purchased the app (either free or paid), then it doesn't matter if the app is installed on any of your current devices. The purchase is in that Apple ID's purchase history and it still has access to both redownload the app and to future updates.

However, the reason this isn't 100% certain is because the developer may choose to no longer offer the app for sale and/or offer the availability of older versions to users who are not on the latest version of iOS. Let me explain with the following scenario.

Scenario

Let's say you purchased app XYZ on an iPhone 6s with iOS 9 installed. You continued to update XYZ from version 1 up to and including version 3. You then purchase an iPhone X (with iOS 11) and decide to start from scratch in terms of what apps you install and you don't install XYZ. In the meantime, the developer of XYZ transfers the app to another developer. This new developer continues to maintain and update the app which is now at version 5.

Apple then releases iOS 13 and the new developer updates XYZ to version 6. However, upon doing so, they decide to edit the list of last compatible app versions so that moving forward only versions 5 and 6 are available for download. However, because you're still on iOS 11, when you try to install the app it isn't available. 

Of course, in the above scenario, you could just update to iOS 12 (or iOS 13) and the app will then be available.

Additionally, as alluded to earlier, the developer may choose to remove the app from sale in which case you also will be unable to install it again.

NOTE:- The original/existing developer of an app can also remove it from sale or edit the last compatible app versions list, in which case the end result would be the same.