Yes, forwarding mail is probably that easy. There is no way however to move yahoo mail archives to gmail which was a popular rumor about 12 years ago.
I dislike gmail but it does allow easy sorting. It's responsiveness can be slow. And google follows you everywhere. The only thing worse for responsiveness is Linked-In.
Yahoo has switched back to struggling with spam filters. I think they are paid to let some spam in. I've had yahoo for more than 25 years, and tire of the conversions to different levels and rules. It's a nightmare for me to extract what I've archived in that account, but I started on the project. I have to download each email individually.
I surely prefer mail.com. I've had that for 20+ years. Easy sorting, quick responsiveness. THey went through a glitchy few days about 2008 when they changed platforms or something, but they've been good otherwise. If my mailbox storage ever fills up there is always their connection to the cloud, or paying a yearly fee which I would do b/c I can't lose this account.