Laziness/cost. It would be more difficult to build app syncing, installing apps from your web browser, counting installs and reviews without spam, purchasing and licensing, etc. without being able to assume there is an associated account to tie it all together. They could partially disable some features, but that would be also be a little more work and still not stop the complaints from people who don't want to sign in.
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I've been wondering for a while: why does google play require a sign-in to install apps?
Mozilla lets anyone download addons from anywhere, likewise I should be able to download an apk to my desktop and install on my phone.
The point is to tie you into the Google ecosystem. That's the entire purpose of Android, really.
Laziness/cost. It would be more difficult to build app syncing, installing apps from your web browser, counting installs and reviews without spam, purchasing and licensing, etc. without being able to assume there is an associated account to tie it all together. They could partially disable some features, but that would be also be a little more work and still not stop the complaints from people who don't want to sign in.