You asked about games that started off disappointing but got better. Most of the time it's the other way around, but I can think of a few. Whoever said Until Dawn was pretty on the ball. It starts off as you might expect as a typical "annoying young adults get bucketed by enigmatic killer" and then the reality warping and gross descent-into-madness imagery gets better after the first "twist" of the game
Don't open this this is you don't want plot spoilers.
Whilst I'm totally biased towards the Forbidden Siren games (see avatar and user handle) they definitely strike me as "gets better the more you invest in it" type games, especially given how bloody difficult they are. Forbidden Siren 2 ditches some of more annoying aspects of the first game though, whilst remaining a challenge. I'm just glad they got rid of the timed missions from the first. Those were frustrating as fuck.
Another horror game that begins rather average (though admittedly atmospheric) is called Unforgiving - A Northern Hymn, a Swedish folklore first-person adventure. I found it rather banal to begin with, wandering around dark woods with a few examples of spooky spirits and humanoid creatures - though the design of which are extremely good. But after learning more about the religious community (I know you have a thing for cults Ross) the game gets subtly and increasingly strange. It has multiple endings too.
If you don't mind something more emotional, artsy and narrative-led (I know how some people feel about walking simulators) then The Beginners Guide definitely subverts your expectations by the time it is done, given that it seems like a technical demo dedicated to the narrators inventive friend Coda. It ends up being a very poignant and effective message about needing validation and fulfillment. I read one youtube comment that summed up the game;
Speaking of Eastern Europe's lax copyright implementation, it reminded of the time I saw a hair/beauty place in town with a banner hung over the door. They had apparently found an image of Kasumi from Dead or Alive in a black bikini and just used that. I found the blatant appropriation rather funny.