I’ve thought about this exact “solution” too, and even tried using it in writing sometimes (not for real people, though). Ultimately, although capitalized singular “They” does its job, and means that one needs to think marginally less about phrasing… It still just feels kind of weird, because of how capitalized pronouns in English are almost always honorific, and are associated particularly with the Abrahamic God. This includes capitalized “You”, for the record. So at the very least, capitalized singular “They” comes across as a bit overly formal; at the very most, it comes across as literally deifying non-binary people.
Rephrasing or clarifying really does solve most of the issues with unclear reference. People who complain about singular “they” being confusing are basically just using the pronoun as a proxy for not wanting to hear about non-binary people. What I think is that the more people use singular “they”, the more people will learn to use the pronoun in a clearer manner, and the more people will find disambiguating shorthands. The reason there’s no standardized way to distinguish singular and plural “you” outside the reflexive, after all, is because the ambiguity of “you” is not enough of a problem to warrant a single standardized solution. I think singular vs plural “they” is going to be the same way, although I’m not confident in this.
Some people probably will use capitalization as a shorthand for number, like you and I thought of independently. More people will use phrases like “they themself” to specify the singular, or “they all” or “some of them” or “both of them” to specify the plural, much like they already do with “you”. At the most extreme I could even imagine “theirsel(f/ves)” being used in place of the nominative or non-reflexive oblique, or people saying “theyse” à la “youse”.
If I may propose something else, though —
Reflexive possessives were once part of Old English and are still used in a lot of Indo-European languages to this day. Taking the Old English words and applying the sound and grammar changes that English went through gives us “sy” and “sine”. So, “She played with sy hair” (i.e. the hair belongs to the person playing with it) versus “She played with her hair” (i.e. the hair belongs to another person).
I think that this could disambiguate a lot of ambiguous pronoun usage in general, not just with singular vs plural they. I also like the sound of using “X sy/sine/s’n Y” as an alternative way of marking possession, in cases where -‘s or -s’ is ambiguous or just doesn’t look or sound right. I don’t use “sy” or “sine” for real people, but I’ve taken to using it for fictional or generic people.