I agree this. This is so important and so easy. I have basically gotten used to those red markers to the point I barely notice them anymore. It is easier to ignore them than to change language every time.
And most IMEs already work with several languages in a way, since they use the sentence context coupled with a system and user dictionary that contains the most common and some set of arbitrary words from any language you want/use regularly enough to have the IME remember the words.
What I described is basically taking that mechanism and baking it into the standard OS without all the custom personalization options the IMEs offer and just offer a ready to use "English + OtherLang" option.
I don't think iOS does anything like that, but there you can still reduce the threshold at which you'll auto-correct and get a significant improvement.
Just goes to show that on all platforms there are still plenty of trade-offs to be explored.
I have a near 50/50 split between two languages in my day to day usage and I would already derive massive benefit from some very small tweaks, ranging from autocorrect accepting words for two languages at the same time to, like I mentioned, just offering prediction with a Markov model trained on two languages simultaneously.
These are fixes that are very easy to implement and would offer a significant benefit, yet they aren't being implemented because the developers just don't care enough.