And especially because the customer is free to order as little ice as they want.

I'm on the opposite end of you - I will always prefer light ice. However! Much like you, there are ice lovers out there who will prefer their drink with extra ice! So yes, to OP: Make the drink to the standard recipe. If they don't like it they can either express their concern and you can adjust on the fly, or they can order it with light ice

The amount of ice can also mess with the proportions. If I’m getting an iced latte with no or little ice and therefore extra milk it waters down the coffee taste and so if someone gives me light ice without me asking them to it changes the taste of the drink

That's actually not correct, this job in fact requires a lot of thinking and sometimes problem solving
Just think about the "human" connections between customers and partners (or even between partners alone), that requires thinking

I'll agree with you on the fact that we don't get paid to make those decisions, there are people (in theory) way more prepared for this subject that get paid more to handle these

I just started a couple weeks ago, but I work at one inside a grocery store and they scold me for every little thing (like giving someone a tall scoop of ice), or filling to the max line instead of the venti line when steaming milk because it often doesn’t fill the cup but “wastes product” :)