In a given discourse, the speaker's choice of begin, begin
on, or a full {begin + VP} when expressing the beginning of
an event associated with a non-eventive NP can be argued to interact
with pragmatic principles, in particular, the Gricean maxim of
quantity (Grice 1975). This maxim says, in essence,
that a speaker should not use more words than necessary to convey a
particular meaning. Given the analysis above, this maxim would ensure
that {begin + NP} will be chosen in all cases for which this
choice does not result in pragmatic conflict, as the lexical entry for
this form is the most specific of any begin entry.
Thus {begin + NP} will be chosen when the event associated with the NP which is to be conveyed fulfills the agentive or telic role of the NP, regardless of the salience of the event in the discourse context. In contrast, {begin on + NP} will be selected in cases for which the event to be conveyed is not the agentive or telic role of the NP, but rather some other event which is clear from context. If the speaker chooses to convey an agentive or telic event with the {begin on} construction, the sentence will still be felicitous if the context suggests the appropriate event, but it is a poor choice of construction given that a more specific form exists which will provide the listener with better clues as to the missing event.
The {begin + VP} form will only be chosen in cases in which the event to be conveyed is neither in the qualia of the NP nor entirely clear from context. The lexical entry for begin in this form provides no clue whatsoever as to the missing event, and if this event is not clear from context it must be explicitly supplied by the speaker.
These suggestions can account for the distribution of these structures in the corpus: the metonymic uses depend on highly conventionalised lexical information and have highly specific interpretations and as such will only be useful in a limited range of contexts, while the {begin on + NP} form requires a very clearly defined context. Both of these situations must occur far less frequently than somewhat vague contexts in which the intended interpretation of a sentence should be made explicit, given the indeterminacies of linguistic discourse (e.g. the reliance by a speaker on a model of the listener's knowledge which might very well be inaccurate). Therefore the relative infrequency of the coercive constructions relative to the more explicit constructions is a result of the varied and underspecified nature of our linguistic environment.