I was wondering what arguments there were to know that P is the head of a phrase [P + N].
As far as adjunct phrases are concerned, we can clearly see that as Ps select Ns (*during the rock; *in the Internet (English isn't my first language, I just assume that's the case based on what I've read and heard), etc.).
But what about Ps being selected by Vs? The following question can be posed: What selects Ns? Let's take the phrase to discriminate against rocks for example. We can find its counterparts without a preposition in other languages. They will presumably all exhibit quite identical selectional properties (e.g. an object being discriminated against can't be inanimate), so I find it unreasonable to assume that some semantic features that define "discrimination" are part of the verb in one language but part of the preposition in the other. For if we assume that, we'll be forced to posit lots of homonymous prepositions to account for various sets they combine with.
The same argument can be used in respect to theta-roles (a beneficiary is unlikely to be a non-living thing).
At the same, there are situations in which the same theta role can be introduced by more than two prepositions for a given verb (to think about v. to think of), and these prepositions may have different sets of selection. If we assume that Vs select Ns via Ps then we will have to create homonymous verbs.
The third option that I find appealing is to assume two levels of selection, the first one being that of Vs, the second one - of Ps.
P.S. One indication of Ns not selectiong Ps comes from causative prepositions in Russian. There's a pair of them (из-за & благодаря) that expresses the speaker's attitude to the desirability of the cause. If Ns determine Ps then their selection occurs beyond them as "desirability" is common for every N so that it doesn't differentiate anything, and is distant from not only their semantics but also from their connotations (which is directed at what they denote).
I hope more competent people comment on that and give a more elaborate explanation if mine wasn't complete and comprehensive.