Yes I agree with you about plenty of other games having weak characters but still being successful because of the gameplay, or the lower quality of stories it'll be compared to in other games, but this game is obviously more setup for a direct translation to a show than most games.
For me the first episode was okay. Probably a 7/10. I wouldnt suggest it to someone else to watch it, but it was a decent enough start to a show about the game. The 2nd episode was great, exactly what I would like to see from a show on the last of us. And it made me want to see the next episode. Then we had episode 3 where I got bored 2/3 of the way through, took a break and then finished it making it the weakest one for me. So now I'm at 1 great episode, 1 okay episode and 1 episode where 2/3 of it lost my interest. So I'm also concerned.
I can see why people who thought the game got boring after a couple of hours dealing with zombies would be happy to insert almost an entire episode into the backstory of a note in the game. But personally I'm watching to see the story I've already experienced adapted and if there are some slight changes that are good ones, great.