I think that the blood hormones will show up quickly (within 2 days) after changing testosterone or estrogen doses. However, the reason to wait longer is because knowing what amount to take is not just about what the blood shows, it's about your symptoms. And your symptoms won't be resolved within 2 days. And you need that info to know what to do with the dose as well, especially the estrogen.
Symptoms can take 8-12 weeks before you know how they're going to stabilise and whether you need more or less estrogen. Or whether you're getting acne or excess hair growth from testosterone.
I think we need to look at both bloods and symptoms. I know it's often said just to treat by symptoms alone up to 100mcg of estrogen, but you need at least 250nmol for bone protection and some women don't absorb different kinds of transdermal estrogen well - so they could be on a 100 patch and not absorbing. And it can take a long time for them to figure that out if they have gradually increased it and waited 8-12 weeks at 100 before doing a single blood test....
For me, I have endo and I don't want to accidentally go too high with the estrogen for that reason too - it might stimulate the endo to grow. I want to find a level that keeps my symptoms away and is over the minimum for bone protection but not to accidentally trial a "higher than really needed" dose. So I am testing before any increase as well - and a few weeks after, too. My GP did the last test but I am going to try Medichecks for the next one, maybe alongside the GP - for accuracy testing.