I bet about 95% of people would disagree with you. This is a very dark pattern, few people are engaging in it, and if you told me non-anonymously that your app does it I would put you and your app on my blacklist of "not to be trusted, ever".
I'm not really anonymous here anyway. Check my profile. It points at my company web page. Feel free to never download any of my games. Please.
FWIW none of my games follow this pattern. But apps live and die based on ratings. I've had people rate my app one star simply because it was a paid version, and the Google return policy at the time was 15 minutes. So the review? "I can't judge whether this app is good in 15 minutes, so I'm rating it one star in protest." [1]
My fledgling, otherwise 5-star app that never even had a single review ask, with its measly ~5 reviews or so, now was pulled down to 4 stars because of one jerk. Who likely downloaded the app to pirate it. Yes, he almost certainly pirated the paid version; it showed up shortly thereafter on pirate sites. And his complaint was specious since I had a free demo you could also download.
We're not talking about voting for a politician here. We're talking about encouraging the people who like an app to vote for it; as I mentioned, the people who hate it already are motivated to slam it. So you're telling me that it's a dark pattern to encourage people who like your app to rate it, and to help the people who are having trouble with your app? Then you have zero empathy or understanding of the life of an indie app developer.
[1] EDIT: Actually, my current app under development is explicitly designed to not care about ranking in the various stores. And it will be Cordova (or similar) based, so I won't need to "reset" the reviews when I push patches to the app. But I don't promise that I won't occasionally ask for a review, so please feel free to blacklist my company and not download it anyway.
If I order a steak at a restaurant and it is overdone, I tell the waiter, I don't eat it and go immediately post a 1 star yelp review. I mention that in the review later on, but their response to my displeasure is part of the review itself.
When you live in a world where reviews can make or break your business, of course you're going to do whatever is possible to encourage good reviews. There's too much riding on it, and too many jerks out there that will rate you 3 stars or less because you weren't exactly right for their needs (or tastes in the case of a restaurant). Because people are going to just not go to a restaurant that rates a 3 star average, and they mostly won't download an app with a 3 star average.
A little bit of reality here: You can't always make everyone happy. You just can't. And because people who are unhappy are something like 7x more likely to leave a bad review than people who are happy, you pretty much have to encourage people who are happy to leave reviews. In other words you have to game the system just to have an accurate review profile.
EVERYONE games the system, even if you don't realize that. Asking for a "fake rating" and then sending them to make the real rating is the obvious way to game the system, and it clearly troubles some people. A far more subtle approach is to just wait for someone to use your app several times over a week and then ask them to rate it. Anyone who's using it that much probably likes it. Halfway in between could be the app that asks you if you're having any problems before asking you to rate it.
But really it's just a matter of degree, and it's life in the app ecosystem, and even in restaurants and other domains today. Railing against it is like railing against the tide.
Sorry, but that particular pattern is 100% appropriate, IMO.
* If someone has a problem with my app, I absolutely don't want to send them to the reviews where they'll post a "tech support review". Yes Apple finally got off their collective behinds and caught up to Google's Play Store in that developers can respond now to reviews, but it's still a terrible venue for helping people with an app. Send them to somewhere that they can get real help, and turn their mediocre to poor review into a positive review.
* If someone has a problem with an app, the odds are roughly 7x greater that they will post a bad review. People who are frustrated are just more likely to seek out the review process to vent their spleens. There's absolutely no reason for me to attempt to be "fair" by reminding everyone to review my app; the haters will find the review button entirely on their own without my assistance.
I might send 4-5 stars to the app store, but if they rate it 3 or less, then damn straight I'm going to ask them what's wrong and not have them rate it. That's just common sense, not gaming the system.