Challenge Problem Set $7$: Why are OVS Languages Rare?

$[$Application of Knowledge; Challenge$]$ Given the basic units of subject NPs $($S$),$ object NPs $($O$),$ and verbs $($V$),$ there are logically $6$ possible word orders of the world's languages: SOV, SVO, VSO, VOS, OSV, and OVS. Of these possible orders, the first two are very common, the second two are found throughout the world but are much rarer, and the last two are almost unheard of$.($The exceptions seem to be limited to a set of Carib languages spoken in South America.$)$ Tomlin $(1986)$ claims that $\backslash (45\backslash \%\backslash )$ of the world's languages are SOV, $\backslash (42\backslash \%\backslash )$ are SVO, $\backslash (9\backslash \%\backslash )$ are VSO, $\backslash (3\backslash \%\backslash )$ are VOS, and less than $\backslash (1\backslash \%\backslash )$ of the world's languages exhibit OSV or OVS. Let's concentrate on the rare OVS order.

Part $1.$ What would the TP and VP phrase structure rules for an OVS language look like?

Part $2.$ Do phrase structure grammars make any predictions about the frequency of word orders? In other words, is there any reason that OVS languages should be rare if they are possible in a phrase structure notation? Does our grammatical system correctly predict that object$-$initial languages should be so very rare?

Part $3.$ Are there any common word orders that phrase structure grammars predict would not exist? $($Assume that subjects are always the NP introduced by the TP rule, and objects are always introduced by the VP rule, and that you can't cross lines in a tree.$)$