"Pushbullet connects your devices, making them feel like one." It's a "sync" program. Pushbullet talks to a lot of things and manipulates a lot of the user's data. So it's inherently a security risk.

Google also has a "sync" program, which syncs things within the Google ecosystem. Google doesn't want others encroaching on their domain. Nor do they want easy import and export from their ecosystem. Although, unlike Apple, they don't come right out and say that.

"If we only published the guilty than no one would be afraid" - attributed to Lavrentiy Beria.