it doesn't teach children to guess what word might fit in the sentence based purely on context, as in mixed methods.
I'm sensing a straw man there. Guessing purely on context? Are you sure?
This is what reduces the debate about reading to shouting over the hedge at your slightly recalcitrant neighbours. Endless claims are made that there is massive research backing the speaker's preferred method, when in fact the studies are anything but conclusive (if you have a coach and horses available, you can have some driving practice with the Clackmananshire study) and the arguments advanced against the speaker's non-preferred method have the distinct scent of freshly cut straw.
Adults, in general, don't read by sounding out. Some do, but they read slowly and with great effort. Adults recognise words like astronaut (to cite an example) and, having seen them before, know what they are automatically. If this were not the case, Japan and China and other countries with partially or largely non-phonetic written languages would have mass illiteracy, when in fact they don't. So at some point successful readers stop reading by "sounding out" and instead read by identifying words completely. Skilled, experienced readers can find a key word in a page of text almost instantly; they are clearly not sounding out the entire contents of the page.
There is an entirely legitimate debate to be had about how people learn to do this, and whether it's a good way to start people reading. And it appears that phonetic methods have more to offer than they were said to twenty years ago, and that the objections raised by the likes of Masha Bell (spelling is irregular) and supposedly fixed by ITA (learn a more regular form) are not as strong as was made out. But it doesn't help anyone to claim that there is no other way to read (clearly, there is, as otherwise there would be mass illiteracy amongst 15 to 40 year olds), nor that the ability to decode from orthography to sounds is the only barrier (there are many other problems of comprehension), nor that people with slightly different views are recalcitrant idiots who just need to be smacked about a bit to see the error of their ways (although it's interesting to see teachers, who normally regard advice from government with scepticism, using "the government approves of synthetic phonics" as though that's the end of the conversation).