Right now, the only game I'm playing that remotely fits the bill would be Deep Rock Galactic; it has seasons and battle passes, but it's also the most player-friendly approach I've seen. It's entirely free, any cosmetics not gained through the battlepass would become available afterwards in the shop (using in-game currency). There's no dailies per se, you have optional challenges to get an extra chunk of XP. But they don't refresh daily, they just cap so you have a maximum of three that will wait for you until they're complete or you swap it for a different challenge. And anytime you complete a challenge, there'll be a cooldown before you can receive a new challenge - so you can't blast through the battlepass too fast.
Also very soon, the devs are adding the ability to select a particular season at will. So if you want, you can jump back into any season and continue its respective battlepass, so it's removed the time pressure to get it done before the next season drops.
I know it gets said a lot, but Ghost Ship Games and their updates to DRG really demonstrate they are the GOAT when it comes to player-focused development... Rock and stone! ⛏