Switch majors in pure math masters in order to apply for a PhD in statistics?
There are a lot of issues here. Whether you get good letters from maths professors is up to them and your relationship with them. Only they can answer that, so you might pose the question to them. Not writing the thesis may impact on that, but only they can say.
As to whether a switch gives you any advantage in application to a US doctoral program, it also depends on that program. Every US university is different in that regard and you can, really, only learn the answer by making application. But I can guess, at least, that you can make it work either way. Math is a good foundation for statistics and the details may matter less than your insight.
But you can plan for both outcomes, at least, by applying now for doctoral programs based on your two year degree while still considering the three year switch. You have a year to figure it out and don't need to make a final decision at this point, I think.
And don't define &quot;top&quot; US universities too narrowly. If you do, you are likely to not get offers. Cast a wide net. There are lots of great US institutions that aren't in the top 10, or even 30, or ...