In a perfect world, all you said would sound great... except it's not a perfect world and that's not how it works in general when switching from one platform to another regardless if it's iOS, Android, Windows, macOS, etc. when using a lot of paid apps. On mobile platforms the Apple App Store and Google Play Store policies prevent paid apps to be transferred between platforms. In reality, it's actually very complicated with many limitations.
Let's pretend for a minute JRiver wanted to do something like this; have a single app license that'd work for both JRemote for iOS and JRemote2 for Android. However, the problems trying to do so are...
1) Apple's App Store and Google's Play Store policies instantly defeat this. You'd think it'd be a really simple thing to accomplish, but Apple nor Google will allow this kind of thing. It doesn't matter if it's a Samsung device, it's an Android device and the Play Store is the main store. Can you imagine Apple allowing users who switch to Android to take their paid apps with them?!? Maybe in Bizarro world or an alternate universe or something, anyways...
2) Licensing for JRemote for iOS is handled by Apple's App Store. Likewise licensing for JRemote2 for Android is handled by Google's Play Store. JRiver themselves really have no control over the licensing on either platform. And as far as I know, external licensing isn't possible with apps in the app stores. I'm assuming because both Apple and Google want a cut of any and all app purchases and transactions (up to 30%, I believe) that they keep a tight leash on any app wanting to make money without going through the app stores. I believe Epic Games' lawsuits against Apple and Google from a year or two ago was because of this very issue, and if I recall they partially lost those lawsuits. It'd be a cold day in hell if Apple especially allowed this kind of thing, unless they're forced by the EU or something like that. If a billion dollar company like Epic Games couldn't do anything about it against both Apple and Google, what makes you think a much smaller company like JRiver could do anything? Which means...
3) JRiver (nor any app developer) has any control or say over Apple's and Google's store policies, nor is it something they can change regardless what you request. It's the same reason they don't have any control or say over refund policies, that's all handled by Apple and Google. And I know what you're probably thinking... why not compensate iOS users who move to Android (or vice versa) with a "gift" of the app on the new platform you moved to? Unfortunately I don't think app developers in general on either platform can "gift" a paid app to a user, so another defeat. Plus maintaining these apps costs money, and they're awesome apps that deserve compensation for all the hard work.
Finally to circle back, JRemote for iOS and JRemote2 for Android are two completely different apps with different codebases, which costs JRiver time and money to develop and maintain. JRemote2 for Android in particular was developed from scratch by Hendrik, which took months of full-time development to get it to the point of public release. All that development time cost JRiver money, and they have to recoup that investment by selling it on the Play Store. If you think about it, that's how software development in general tends to work, it's very common. Think of it as an investment to help keep JRemote2 development going, whereas with a free remote app like Gizmo that hasn't received any updates in years as far as I know. Gizmo does work fine though even today, but I believe there's some very minor issues with it and missing features, like Cloudplay and gapless playback if memory serves. Plus the JRemote apps are a one-time purchase for a price that isn't unreasonable at all, and not a yearly subscription or something like that.
I'll give you a personal example here. I use the paid app RadarScope on Android for weather radar and following severe weather outbreaks and I paid $9.99 for it on the Play Store. If I switched to an iOS device, I know I'd have to bite the bullet and pay $9.99 again for the same app I already bought on Android to use it on iOS. Yes, I'd be a little unhappy about it but at the same time I'd also know there's nothing the RadarScope developers could do about this if I lodged a complaint. Honestly I'd be surprised if they even responded to the complaint, they might just ignore me if I did. Anyways, RadarScope is also available on Windows via the Microsoft Store for $29.99 which is three times the price of the mobile apps, and guess what? I still bought it for that price. It's also $29.99 on Apple's App Store for macOS and yeah I bought it there too when I was using a Hackintosh still. I still could complain about it I guess, but honestly it's pointless to do.
So yes, it sucks having to repurchase paid apps after switching platforms. It'd be even worse if you had active subscriptions (like Netflix or something) through Apple's App Store then switching to an Android device. You'd have to cancel the subscription through Apple and re-sign up on the subscription service's website or through Google's Play Store if they do that sort of thing. Regardless how you or anyone else feels about it, it doesn't change the fact that there's nothing JRiver themselves could do about it and honestly most users know and accept that when switching platforms. You're probably finding this out more if you have a lot of paid iOS apps and finding out they're not transferable between platforms and you'll have to repurchase them if you want to continue using them on Android. There are alternatives to JRemote2 for Android though, like the aforementioned free Gizmo app or even using Panel through a web browser, or you could just bite the bullet and get JRemote2 for Android, it's an awesome app and totally worth it, in my honest opinion.
Otherwise, them's the breaks I'm afraid.