This is mostly because boric acid is commonly believed to have different acidity mechanism. While common acids generally dissociates
$\ce{HNO3 <=> H+ + NO3-}$
boric acid is commonly believed to associate with water
$\ce{H2O + B(OH)3 <=> H+ + [B(OH)4]-}$
this type of acidity is rather common for metal hydroxides, hence the way of writing.
For that matter, not every hydrogen should be written at the beginning of a formula of an acid, but only actually acidic ones. So, $\ce{H2SO4}$, but $\ce{HPH2O2}$