As you point out, the first example follows a similar structure to a newspaper headline. These usually omit auxiliaries, pronouns, articles, and conjunctions, to make a punchy sentence that can be quickly read and understood. However, I think it actually goes with the 2nd and 3rd examples as bullet-points lifted from a political manifesto.
When bullet points are used, the idea is that each bullet point can be linked back to a leading statement, for example:
We promise to:
- Bring companies back into public ownership.
- introduce a shorter working week within a decade
- invest billions to upgrade every home to be energy efficient.
You will notice that I have reworded your first 3 examples slightly to make them form coherent sentences with the leading "we promise to...". The fact is that many bullet-pointed lists dispense with that format for the same reason that newspaper headlines are not always grammatical - the author wants them to be punchy.
The last example reads like an advertisement, like the kind found in newspaper classified sections, and again these follow a similar structure to make key points stand out. Traditionally, classified advertisements in newspapers allowed for 2 or 3 words to be emboldened as a header, so you would want to use important words first, even it means dispensing with grammar.
Example:
I AM A
skilled sports therapist
who about cares about more than just your money
Vs
SKILLED SPORTS THERAPIST
who about cares about more than just your money
Someone looking for a sports therapist will hopefully spot the second advertisement at a glance, whereas the first one might escape their notice.