"I like the games where you click the little men and order them around."
Just like in real life.
Anyway, here's what is on my phone right now. I'm sure you have some of these and a few have expansions if you feel the base game isn't enough.
30 Second Life
Brief History of the World
Chainsaw Warrior: Lords of Night (There's also the first one just called Chainsaw Warrior which is a digital version of the boardgame)
Elder Sign Omens (Has expansions. Digital boardgame)
King of Dragon Pass
Neuroshima Hex! (Has expansions. Digital boardgame)
Out There Omega: The Alliance (This is the most updated version of the game)
Queen's Wish (Spiderweb RPG)
Seedship (Got a few updates minor updates)
Talisman (Digital boardgame which has a shitload of expansions, if you want something more mission based in the same setting there is also Talisman Origins which has a sizable amount scenarios with you guessed it more scenarios you can download.)
Waterdeep (Has a couple small expansions. Digital boardgame)
iWestnoth (Has a bunch of free scenarios available for download)
I don't think these are available on the phone, but I'll list them since I either have or had them on my ipad so if you see them avilable for your phone, you probably should take a look.
Small World (Has a few expansions. Digital boardgame)
Qvadriga (Chariot racer manager sim, you also control your chariots during the races, upgrade the drivers, chariots, horse, etc)
There is also Warhammer Quest 1 & 2 which are basically dungeon crawlers where you go in with your adventurers and get loot, level up, repeat.
I remember you saying being interested in Mars, well there's a digit version of the boardgame Terraforming Mars which is exactly what it sounds like. Manage resources trying to beat the other players to settling Mars, etc.
Further searching will result in more digital boardgames. They've been doing a lot of digital versions of them over the years.
Underhanded is basically a ghetto Cultist Simulator, but it has the advantage of being a mobile game that's free and has no ads or monetization. Unfortunately once you've beaten the game there's not a lot to do besides kill people and see how many relics you can have in your hand at the same time.
DAN BALL is a cool dev from years and years ago that also has fun free and adless games, but they're based on individual pixels. Not too much of a problem on PC where the screen is big, but on phone the little physics-based stickmen can strain your eyeballs
Oh, yes. I really liked this demon's screaming expression, though it doesn't come across too well when it's all compressed on the forums.
I feel like I've seen that pic before somewhere. Like some horror magazine or old RPG rule book.
It's actually a Henry Justice Ford drawing. He's a guy who used to illustrate a lot of fairy tales and whatnot in a pretty cool way. I forget what exact story this was from, just that these guys were somewhere in the background and I liked them a lot.
Exiled Kingdoms is a fun old-school rpg although it's better on desktop.
I remember geometry dash being pretty good. It's like a cross between a rhythm game and a platformer. And there's also a few games like Fez, Stardew Valley, and Terraria that got ported over, though I can't imagine why anyone with access to a real computer would choose to play them on a phone. But yeah, most of the stuff on the App store is pretty trash nowadays because of in app purchases and whatnot. I think the reason mobile games specifically are problematic is because a lot of their market is, as you said, eight year olds and Facebook moms who don't know any better. If the only games you play are bad ones, then you'll never think to question whether they can actually be better. I used to spend a lot of time playing mobile games when I was little, especially Pokemon clones. I remember the first time I picked up a REAL Pokemon game, the fact that I didn't have to wait two hours or pay in order to heal after a battle blew my mind. But if I'd played nothing but mobile games my whole life, I'd never have known the difference.
It also probably doesn't help that people expect mobile games to be free, so the developers have to find other ways to make a profit.
The Powder Game and most of its clones don't have ads iirc. There's also a pretty easy and customizable strategy game about Hexagons called Antiyoy which doesn't have any ads and garbage.
Wasn't there a free DS emulator? Or, at least it was paid-optional. The people behind My Oldboy would tend to do stuff like that, where you were allowed to use the emulator for free, but emulator perks like speeding up the gameclock and using gameshark codes are paid options.
If you dig Cards against Humanity you might like Evil Apples. I haven't played it in a while but if I remember correctly it's free with minimal ads. The only thing that sucks is waiting for other players to put cards in. They might've added a time limit of like 30 secs to make sure games don't take days to do. There's different card packs you can get by using the in-game currency by playing and winning. Overall pretty fun if you're just looking for some casual.