I certainly can log in on a laptop with my ESPN credentials, but it would not give me access to ESPN3 or any ESPN channels. I did pay for ESPN+, so my ESPN credentials would give me access to that. I do not authenticate with a tv provider sign in as I do not have a cable subscription of any kind; that would give me access to ESPN content on the website.
My access to ESPN3 is authenticated over my internet connection. I get access through AT&T, my internet provider, and for whatever reason as part of their deal I am only given access to ESPN3 over OTT streaming devices. So phones, tablets, laptops do not work. I found this answer a long time ago on reddit. Honestly, I did not originally know I had ESPN3 when I got my Roku device a couple of years ago. I came across it by accident.
However, yes, your solution of signing up for a cable tv/streaming tv provider would probably allow me to access ESPN3 on my laptop. I will consider that. Since another user who had YouTube TV could not access ESPN3 on the ESPN app on Roku, I am assuming that means the YouTube TV app does not have access to the same replays that ESPN3 has? So I am assuming using the Roku app for YouTube TV still wouldn't change that issue? Thanks!
Also, since ESPN3 is a streaming only channel and was traditionally not part of a cable package, I wonder if that's part of the problem on the Roku app? It was originally only offered to people who had high-speed internet access with an internet provider that paid fees to ESPN. It probably still authenticates over the internet for everyone, even people with a cable package. Maybe some update ESPN did through their app this year messed it up. Does anyone who has a cable package have problems connecting to ESPN and ESPN2 replays on the ESPN app on Roku? Just curious.