PPer Cambridge Dictionary Online,
commit verb (PROMISE)
[I or T] to promise or give your loyalty, time, or money to a particular principle, person, or plan of action:
Like so many men, he has problems committing himself to a relationship.
The government must commit itself to improving healthcare.
Question is, would it be grammatically acceptable to rephrase the example sentences above as follows, while keeping the exact same meaning?
Like so many men, he has problems committing to a relationship.
-and-
The government must commit to improving healthcare.
The government must commit itself to improve healthcare.
The government must commit to improve healthcare.
EDIT:
Please, consider this other example:
We commit ourselves to providing […]
We commit to providing […]
We commit ourselves to provide […]
We commit to provide […]
Best Answer
These look like examples of noun ellipsis, where a contextually-recoverable noun is removed from the sentence.
Yes, the form in each case strongly suggests that the dropped noun is the closest grammatically preceding noun.
You show an example with more than one noun phrase (so many men, he):
The noun grammatically closest to and preceding the phrase committing to is he, so the person that "he" has problems committing to a relationship is himself, not the many men, and not some unmentioned person.