That depends on interpretation of 'good' and 'strategy'.

Bloons Tower Defence 5 is fairly well known as something you can outright purchase, and complete without IAP. Unfortunately it still has them... And TD doesn't tend to be for beyond casual gamers. (What is good strategy?)

Shattered Pixel Dungeon is a fine rogue, without IAP. Nothing special, nothing terrible.

I found Enchanted Fortress somewhat addictive. No IAP. Somewhat simple premise, but decent execution.

Was gonna say the Harebrained Schemes' Shadowrun ports are pretty good (Dragonfall and Returns) but can't seem to find them on the Play Store now. Weird.

There's also the XCOM: Enemy Within port for Android. I loved these.

XCom is a fantastic mobile port of a truly great game. Depending how far you want to stretch the definition of strategy there’s also Stardew Valley.

Rebel Inc.: https://www.ndemiccreations.com/en/51-rebel-inc

It has a few in-app purchases, but they’re just to unlock various maps and characters if you’d prefer not to have to earn them by winning earlier stages first. There’s no grinding, no ads, no “diamonds”, none of the usual mobile-game BS.

If you like board games at all, there are a ton of board game adaptations. The unique thing about board game apps is they seem to be one of the few categories of games that can still get away with charging money up front for their audience, and not having any free to play garbage in them. They're about the only apps I still get for mobile platforms, nowadays.

Twilight Struggle, for example, is a very thematic and deep board game about the Cold War, that for years was the highest rated game on BoardGameGeek, and they made a great version for mobile. By the way, the board game was designed by Ananda Gupta also designed the video game XCOM: Enemy Within. https://www.pockettactics.com/reviews/review-twilight-strugg...

Through the Ages is another popular and deep strategy board game that's about building up civilizations over time, and it has a really excellent mobile version (so good that a lot of people prefer it to playing the board game version): https://www.throughtheages.com/

Race for the Galaxy is another good one, where you're trying to build up an engine, but faster than your opponents. Has tons of cards with unique properties and yet it plays pretty quickly. https://www.pockettactics.com/reviews/review-race-for-the-ga...

Pandemic is another modern classic game about trying to keep four different viruses contained as well as possible around the planet while searching for a cure. It's a bit lighter than the others I mentioned mechanically, but it can still be a tricky puzzle of efficiency, trade-offs, and pushing your luck, especially at higher difficulty levels: https://www.pockettactics.com/reviews/review-pandemic-board-...

There's a section on BoardGameGeek for iOS Board Game news (seems to also have Android and Steam in there also) that is my usual go-to to find out what board games are being adapted to mobile. Here's the link: https://boardgamegeek.com/blogcategory/108

DEFINITELY not for everyone but Girls Frontline is a less idly idle game. There are dailies which you can do to get items, and logging in every day gives you stuff. There are microtransactions to get the stuff you need fast, but even with all the money in the world you still need some grinding to beat the game.

Here's a starting point:

The Best Offline Strategy Games For Android & iOS: https://www.pockettactics.com/guides/offline-strategy-games-...

Not sure if this fits within your definition of strategy, but Mini Metro is a great example of a game that "works" on mobile.

https://dinopoloclub.com/minimetro/

I liked Hoplite [0] for some time.

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[0]: https://itunes.apple.com/us/app/hoplite/id782438457?mt=8

Polytopia. Heroes

Antiyoy - or polytopia. Two things that are good for a 5 minuite or 15 minuite game